A Graphical Approach to College Algebra (7th Edition)
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Any particular term of the sequence is equal to ... more
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for ; The number of ancestors of the insect in a ... more
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The expression for the population density of the ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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; Sequence is a list of ordered numbers which ... more
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Sequence is a list of ordered numbers which ... more
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Both the sequence and functions are mathematical ... more
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A sequence is said to be a finite sequence if its... more
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A sequence is said to be a finite sequence if its... more
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A sequence is said to be a finite sequence if its... more
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The sequence has only 4 terms so it can be written... more
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There are inifinitely many numbers in the sequence... more
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There are infinitely many numbers in the sequence ... more
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First term and the formula for the together give ... more
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The definition of the sequence gives the first two... more
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; First term is given to be and the recursion ... more
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; First term is given to be and the recursion ... more
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; First two terms of the sequence are given to be... more
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; First two terms in the sequence are given to be... more
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; First term of the sequence is given to be . The... more
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; First term of the sequence is given to be and ... more
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; First two terms of the sequence are given to be... more
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; First two terms of the sequence are given to be... more
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35 ; The summation to be calculated is . For each... more
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51 ; The summation to be calculated is . For each... more
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; The summation to be evaluated is . For each ... more
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; The summation to be evaluated is . For each ... more
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288 ; The summation to be evaluated is . For each... more
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701 ; The summation to be evaluated is . For each... more
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3 ; The summation to be evaluated is . For each ... more
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; Since and Now first target to calculate ... more
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; For evaluating terms of for the function , ... more
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; For evaluating terms of for the function , ... more
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; For evaluating terms of for the function , ... more
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600 ; Using the summation property ; where is a ... more
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10 ; Using the summation property ; where is a ... more
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1240 ; The expansion of summation rule is . In ... more
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3251250 ; In the given expression of series, the ... more
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90 ; In the given expression of series, the ... more
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115 ; In the given expression of series, the ... more
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220 ; In the given expression of series, the ... more
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-58 ; In the given expression of series, the ... more
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304 ; In the given expression of series, the ... more
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973 ; In the given expression of series, the ... more
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3201280 ; In the given expression of series, the ... more
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411424 ; In the given expression of series, the ... more
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363055 ; In the given expression of series, the ... more
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94796 ; In the given expression of series, the ... more
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; In the given series, the number of terms ... more
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; In the given series, the number of terms ... more
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; In the given series, the number of terms ... more
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; The signs are negative for odd terms and ... more
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Converges to ; The first ten points for the graph ... more
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Converges at 2 ; The first ten points for the ... more
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Diverges ; The first ten points for the sequence ... more
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Diverges ; The function diverges, as the value of... more
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Converges at 5 ; The given function converges ... more
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{1,2,3,4,5,6,7,8} ; The positive integers which ... more
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1,2,3 ; The positive integers which satisfy the ... more
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1,2,3,4 ; The sequence needs to be greater than or... more
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All integers above 29 ; The given sequence is ... more
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1. The sum of first six terms of the series = 1.... more
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500,400,320 ; The population for is as per given... more
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An arithmetic sequence can be either increasing( ... more
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; Formula is given as:This implies that can be ... more
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; Formula is given as:This implies that can be ... more
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; Formula is given as:This implies that can be ... more
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; Formula is given as:This implies that can be ... more
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; Formula is given as:This implies that can be ... more
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; Formula is given as:This implies that can be ... more
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; term of an arithmetic sequence is given as:,... more
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; term of an arithmetic sequence is given as:,... more
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; term of an arithmetic sequence is given as :,... more
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; term of an arithmetic sequence is given as :,... more
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; Find . ; term of an arithmetic sequence is ... more
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; Find the common difference, ; Formula is given ... more
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; In arithmetic sequence the formulae of term is... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula of term is ... more
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; In arithmetic sequence the formula for sum of n... more
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; In arithmetic sequence the formula for sum of n... more
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; In arithmetic sequence the formula for sum of n... more
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; In arithmetic sequence the formula for sum of n... more
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; ; Substitute a_n in the given inequality ; ... more
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; ; Substitute value of in the inequality ; ... more
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; ; Substitute value of in the inequality ; ... more
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; ; Substitute value of in the inequality ; ... more
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; , where n is the number of terms, is the first... more
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90 ; ; ; , where n is the number of terms, ... more
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; ; ; ; ; , where n is the number of ... more
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; ; ; ; , where n is the number of terms... more
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; Finding and ; ; ; , where n is the number... more
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; Finding d and ; ; ; ; , where n is the ... more
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77.5 ; ; , where n is the number of terms, is ... more
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-46.25 ; , where n is the number of terms, is the... more
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; ; , where n is the number of terms, is the ... more
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; ; , where n is the number of terms, is the ... more
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; ; , where n is the number of terms, is the ... more
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; ; , where n is the number of terms, is the ... more
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The domain of the sequence is, {1,2,3,4,5,6} and ... more
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The domain of the sequence is {1,2,3,4,5} and the ... more
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The domain of the sequence is {1, 2, 3, 4, 5, 6} ... more
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The domain of the sequence is {1, 2, 3, 4, 5} and ... more
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Equation : Domain:Range: ; From the graph we can ... more
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Equation : Domain: Range: ; From the graph we can ... more
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80 ; Find common difference ; Find the total ... more
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21 ; Find common difference ; Find the total ... more
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1275 ; Find common difference ; Find the total ... more
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2401 ; Find common difference ; ; Find the total... more
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4070 ; Find common difference ; ; Find the total... more
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837 ; Find the common difference by applying the ... more
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4100 ; Calculate common difference ; Give ; Find ... more
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-3775 ; Calculate the common difference ; Given ; ... more
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18 ; Find the first term of the series ; Given ; ... more
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-25 ; Find the first term of the series ; Given... more
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140 ; Find the first term of the series ; Given... more
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465 ; Find the first term of the series ; Given... more
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-684 ; Find the first term of the series ; ... more
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-817 ; Find the first term of the series ; Given... more
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500500 ; Find the first term of the series ; ... more
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2001000 ; Find the first term of the series ; ... more
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328.3 ; The sum of the given series can be ... more
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824.9 ; The sum of the given series can be ... more
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172.884 ; Calculating a1 and a10 ; ; Sum of ... more
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-60.849 ; Calculating a1 and a10 ; ; Sum of ... more
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; First Term of the series = a1, k=1Last Term of ... more
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; First Term of the series = a1, k=1Last Term of ... more
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n<6, largest value of n=5 ; First Term of the ... more
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n<4, Largest value of n=3 ; First Term of the ... more
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1281 ; First Term of the series, a1 = 51Last Term ... more
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429 ; First Term of the series, a1 = -8Last Term ... more
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4680 ; For half a day, the clock chimes 12 times(1... more
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465 poles ; Here, First Term of the series, a1 = ... more
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54,220 people ; First Term of the series, a1 = 49,... more
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; First Term of the series, a1 = 2Last Term of ... more
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; First Term of the series, a1 = 18Last Term of ... more
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$600 ; As given, First Term of the series, a1 = ... more
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Any sequence with all the terms equal like ; For ... more
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It is because the value of d, the common ... more
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; As given, ; ; As given, ; ; Subtract(1) ... more
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The problem with technology here is that the ... more
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; The general formula for finding the in a G.P. ... more
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; The general formula for finding the in a G.P. ... more
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; Since, two corresponding terms in a G.P. series... more
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; Since and are given, divide by to get the ... more
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; It is known that . Use this formula to get . ; ... more
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; To find use the formula, . ; To find use the ... more
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; First, find the first term of the series by ... more
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; First find the first term of the series by ... more
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; Find the first term of the series by using the ... more
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; Find the first term of the series using the ... more
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; Given the first term of the series as , the ... more
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; Given the series and the first term, find the ... more
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; Since in the given sequence the terms are given... more
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; Since the G.P. sequence is given, use to get ... more
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; Since the G.P. sequence is given, use to find ... more
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; Since the G.P. sequence is given, use to find ... more
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; From the given inequality it is clear that when... more
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n= ; From the given inequality, it is visible that... more
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n=1,2,3 ; From the given inequality, it is clearly... more
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125, ; The formula is used to find the term of ... more
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, ; The formula is used to find the term of ... more
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, ; The formula is used to find the term of ... more
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682 ; If is a geometrical series then the ... more
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1364 ; If is a geometrical series then the ... more
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12.375 ; If is a geometrical series then the ... more
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Aprroximately 860.95 ; The formula is used to ... more
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Approximately ; The formula is used to find the ... more
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363 ; If is a geometrical series then the ... more
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30 ; If is a geometrical series then the ... more
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; If is a geometrical series then the expansion ... more
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; If is a geometrical series then the expansion ... more
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688 ; If is a geometrical series then the ... more
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-14769 ; If is a geometrical series then the ... more
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-508 ; If is a geometrical series then the ... more
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315 ; If is a geometrical series then the ... more
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1820 ; If is a geometrical series then the ... more
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; The series describes the sum of first terms of... more
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; The series describes the sum of first terms of... more
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When the converges to a real number. ; By adding ... more
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1 ; The series describes the sum of infintie terms... more
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; The series describes the sum of infinite terms ... more
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; The series describes the sum of infintie terms ... more
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; The series describes the sum of infinite terms ... more
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. The sum converges ; The series describes the sum... more
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. The Sum converges. ; The series describes the ... more
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. The sum does not converges. ; The series ... more
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. The sum does not converges. ; The series ... more
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; The series describes the sum of infinite terms ... more
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27 ; The series describes the sum of infinite ... more
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; The series describes the sum of infinite terms ... more
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256 ; The series describes the sum of infinite ... more
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; The series describes the sum of infinite terms ... more
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0.15 ; The series describes the sum of infinite ... more
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; Let and Therefore Now compute value for Since ... more
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; Let and Therefore Now compute value for Since ... more
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; Let therefore is geometric sum of first -term... more
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; Let clearly is geometric sum of first -term ... more
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; Let Substitute in ; more
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13.42 ; Total chemical = of draining and that much... more
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; initial molecules ;The molecules will half ... more
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26214.4 ; Inital cost loss by 20% so, cost after ... more
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; 337.5 ; so the geometrc sequence, For n=4 ; more
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; Solution When the ball droped the height is 10 ... more
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16 ; 512 ; First generation second generation (... more
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3 milligrams ; Amount of drug left in the body ... more
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; Second equilateral triangle is made by joining ... more
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, , forms geometric series with common ratio . ; ... more
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The series , , , , ...... forms a geometric series... more
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2 ; factorial is given by .Thus, calculate . ; more
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6 ; And, ; more
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120 ; and ; more
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56 ; can be written as .Thus. ; more
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The given property holds true for all positive ... more
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5040 ; more
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720 ; P(10,3) = can be written as ; more
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84 ; can be written as ; more
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495 ; can be written as Thus ; more
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560 ; Here, n=16 and r=3 Thus, ; more
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1860480 ; The expression is going to be evaluated ... more
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9034502400 ; The expression is going to be ... more
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259459200 ; The expression is going to be ... more
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863040 ; The expression is going to be evaluated ... more
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15504 ; The expression is going to be evaluated by... more
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75287520 ; The expression is going to be evaluated... more
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6435 ; The expression is going to be evaluated by ... more
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35960 ; The expression is going to be evaluated by... more
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a-Permutationb-Permutationc-Combinationd-... more
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The difference between Permutation and Combination... more
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30 ; Using the fundamental principle of counting, ... more
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840 ; Using Fundamental Principle of Counting, 7 ... more
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120 ; Using the fundamental principle of counting... more
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15 ; Using the fundamental principle of computing... more
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120 ; Using the fundamental principle of computing... more
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; Given that we need to seat 6 people in a row ... more
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; Its required to find the total number of ways ... more
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; In this question its required to find the ... more
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; It's required to find that how many possible ... more
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; Its given that there are 15 members in a club ... more
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; Its given that there are 20 players and to find... more
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; Its required to find possible number of ways ... more
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; Given that its required to find the number of ... more
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; Its required find total possible number of 4-... more
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; There are 25 apples present in the crate. Now ... more
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. ; The various contents inside the Burgers are 6... more
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; Three people are selected from a group of 12 ... more
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; Given the bag contains 15 marbles and its ... more
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10 ; From numbers 1,2,3,4 and 5, 2 cards are to be... more
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28 ; Total number of marbles = Total number of ... more
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; Total courses = ; Courses to be selected ; ... more
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; Pineapples in crate = ; Pineapples to be drawn... more
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; Total number of ingredients = ; Ingredients ... more
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; Number of assistants = ; Assistants to be ... more
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; Number of seats = Number of children = ; That ... more
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; Selecting men from men. ; Selecting Women ... more
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; Since every elected person will have a ... more
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4096 ; During coding, the first switch can be set ... more
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64,000 ; The first number can be any number ... more
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1,000,000 ; The first number can be any number ... more
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1000 ; The first number to be picked can be any ... more
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6 ; Since in circular arrangements the clockwise ... more
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720 ; Since in circular arrangements the clockwise... more
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First, simplify the expression given on the left-... more
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Simplify the expression given on the left-hand ... more
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Simplify the expression given on the left-hand ... more
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Simplify the expression given on the left-hand ... more
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Simplify the expression given on the left-hand ... more
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Simplify the expression given on the left-hand ... more
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Simplify the expression given on the left-hand ... more
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First, simplify the expression given on the left-... more
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For the terms in the binomial expansion, when the ... more
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120 ; For any positive integer the factorial is ... more
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10 ; For any positive integer the factorial is ... more
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35 ; For any positive integer the factorial is ... more
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56 ; For any positive integer the factorial is ... more
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56 ; Apply formula of binomial coefficient when ... more
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35 ; Apply formula of binomial coefficient when ... more
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45 ; Apply formula of binomial coefficient when ... more
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84 ; Apply formula of binomial coefficient when ... more
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1 ; Apply formula of binomial coefficient when ... more
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1 ; Apply formula of binomial coefficient when ... more
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56 ; Apply formula of binomial coefficient when ... more
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36 ; Apply formula of binomial coefficient when ... more
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4950 ; Apply formula of binomial coefficient when... more
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15504 ; Apply formula of binomial coefficient when... more
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1 ; Apply formula of binomial coefficient when ... more
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1 ; Apply formula of binomial coefficient when ... more
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; Apply formula of binomial coefficient when ... more
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; Apply formula of binomial coefficient when ... more
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9 ; Expansion of contains terms.Here the value ... more
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11 ; Expansion of contains terms.Here the value ... more
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First term is Second term is ; Using binomial ... more
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When combination of elements choose ; term of ... more
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; Expansion of . can be written as . Here value ... more
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; Using the formula of binomial theorem, ; ... more
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; Formula for finding rth term of binomial having... more
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; Formula for finding rth term of binomial having... more
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; Formula for finding rth term of binomial having... more
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; Formula for finding rth term of binomial having... more
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; Formula for finding rth term of binomial having... more
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; Formula for finding rth term of binomial having... more
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; Formula for finding rth term of binomial having... more
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; Since there are total 12 terms in the binomial ... more
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; Comparing both sides this implies that . ; more
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; Since for the power of to get 4 the power ... more
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approximately. ; more
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30104.38130.83 approximately ; more
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Exact value=479,001,600Approximate value=475,687,... more
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Exact value=6,227,020,800Approximate value=6,187,... more
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0.942approximately ; more
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0.826 approximately ; more
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1.015approximately ; more
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1.006 approximately ; more
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24 ; There are four items to put at the first ... more
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3,628,800 ; In this arrangement order matters. For... more
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210 ; more
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210 ; more
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450 ; Since there are 6 choice for guards ... more
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72 ; Since there are 9 basic plans. Therefore ... more
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; Since .Therefore, there are total terms in the ... more
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; Apply on and get .Apply on each coefficient in... more
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; Since r-th term in the binomial expansion of ... more
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; Note that the rth term in the expansion of is ... more
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positive integers. ; Mathematical induction is a ... more
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No, it can be concluded that the proof is complete... more
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1 ; 2 ; Evaluate and for positive integers See ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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Proof by mathematical induction has two steps ... more
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For n=1 it is true,To prove The equation for ... more
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The given statement is not true for these ... more
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The given statement is not true . ; If n=1 the ... more
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None of the positive integer value of n is not ... more
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The given statement is not true for these ... more
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For n=1, The statement is true.=To prove consider... more
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For n=1, The statement is true.For n=k, The ... more
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For n=k, The statement is true. To prove ... more
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For n=2 the result is true For n=k, The statement ... more
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For n=1 then statement is true where a>1 this ... more
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For n=1 then the then statement is true where a>... more
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If 0more
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If then let represent For n=4 24>16 is true ... more
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If then let represent For n=4 24>16 is true ... more
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for n=5 thenn=k this results true for To prove... more
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At each stage, the length of the sides of each new... more
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Let there be 2 rings in peg A.To move the rings to... more
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Since the sample space is the set of all possible ... more
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The sample space is the set of all possible ... more
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The sample space is the set of all possible ... more
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The sample space is the set of all possible ... more
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The sample space is the set of all possible ... more
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The sample space is the set of all possible ... more
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Since the probability of an event is given by ... more
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0.143 ; Here, .And also,Therefore, the probability... more
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; Let represent getting a hit. The probability of... more
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; Let represent sum of the number on two slips is... more
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; The odds that it will rain is given as. Let ... more
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; The odds that the canditate will win is given ... more
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; )-For any event ,, So cannot occur)-When the ... more
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499 to 1 ; Let be the event of bank will make a ... more
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; The probability of picking a heart as a first ... more
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; The probability of getting heart as a wrong ... more
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0.72 ; Let be the total number of workers in the ... more
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The probability of event is nothing but the ratio ... more
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0.3125 ; In the family, a child either will be a ... more
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0.03125 ; In the family, a child either will be a ... more
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0.5 ; In the family, a child either will be a boy ... more
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0.96875 ; In the family, a child either will be a ... more
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0.042(approximately) ; The probability of a person... more
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; A die has 6 faces numbered 1,2,3,4,5,6The ... more
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0.00663(approximately) ; A die has 6 faces ... more
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0.875(approximately) ; A die has 6 faces numbered ... more
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0.3813(approximately) ; A die has 6 faces numbered... more
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0.49 ; The probability of student selected will be... more
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0.952 ; As we have calculated in part (a)the ... more
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XY00.01510.09320.23430.31540.23450.09360.015 ; As ... more
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; As given,odds 5-6 with every bet will be ... more
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; A coin has 2 sides and If one coin is flipped ... more
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; Let the probability of not drawing 4 aces and 1... more
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; Let is the event of the graduate selected at ... more
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3)First five terms are . can be rewritten as . is ... more
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; Using the nth formula of arithmetic sequence. ... more
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; Use the nth term formula of arithmetic sequence... more
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; Use the common ratio formula to find first five... more
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; Find the common ratio of the sequence from the ... more
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; ,since we need to add , the common difference, ... more
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; Use the formula for nth term of geometric ... more
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; We want the sum of first 12 terms. ; more
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; Find the first term using the common difference... more
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; The fifth term could be found by using the ... more
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; Find the value of using the formula and ... more
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; Find the common ratio using the formula with ... more
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; When a ball is dropped, it rebounds to 90% of ... more
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The Sum of given ; We have a1=1 and r=-1 ; more
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6.0833 ; Evaluate the Sum of the expression For ... more
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; We have ; ; We have j=10 ; more
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; We have, ; ; Now, j=2500 ; ; more
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; We have ; Now, ; more
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It is a divergent series. ; We are given, ; Here... more
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The sum of the series ; We have the series ; In ... more
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The given series is divergent. Hence, Sum does not... more
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; We have the series ; Now we need value of n ... more
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; We have the series ; Now Since it is a GP, then... more
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; To calculate 9! , ; more
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; To calculate P(9,2) ; more
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1 ; Evaluate that means calculate permutation ... more
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252 ; Evaluate that means calculate combinations ... more
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56 ; Evaluate that means calculate binomial ... more
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Yes ; Student identification number is the ... more
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; Expansion of binomial theorem is given by And ... more
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; Expansion of binomial theorem is given by And ... more
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; Expansion of binomial theorem is given by And ... more
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; Expansion of binomial theorem is given by And ... more
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; If binomial expression is then term is given ... more
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; If binomial expression is then term is given ... more
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First term is Second term is Third term is Fourth... more
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Fifteenth term is Sixteenth term is Seventeenth ... more
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Those statements which hold every natural number ... more
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Mathematical induction has two steps as follows:... more
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Mathematical induction has two steps as follows:... more
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Mathematical induction has two steps as follows:... more
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Mathematical induction has two steps as follows:... more
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Mathematical induction has two steps as follows:... more
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48 ; Here, one event is chapels which has ... more
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90 ; Here, one event is styles which have ... more
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24 ways. ; Suppose four students are assigned to 4... more
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504 ways ; Suppose a state wide tournament has 9 ... more
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456,976,000 ways and 292,032,000 ways. ; Assume a ... more
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. ; Consider a card is drawn from the standard ... more
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. ; Consider a card is drawn from the standard ... more
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. ; Consider a card is drawn from the standard ... more
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Approximately 0.2961. ; Suppose a die is rolled 12... more
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None of the series is an arithmetic progression ; ... more
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The difference between the second and first term ... more
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24 different types of shoes ; Let the four styles ... more
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6840 ; The club has 20 members.The post of ... more
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6160 ; There are 8 men and 12 women in the club.2 ... more
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