InterviewSolution
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InterviewSolution
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The sequence of odd natural numbers is divided into groups `1,3,5,7,9,11,"…."` and so on. Show that the sum of the numbers in nth group is `n^(3)`. |
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Answer» Sequence of natural number is divided into group 1,3,5,7,9,11… ` therefore ` nth row contains n elements 1st elements of nth row =`n^(2) -( n-1) ` Least elements of nth row ` =n^(2) +( n-1) ` ` therefore `Sum of the element in the nth row ltbr gt ` = (n)/(2) (a+l) =(n)/(2) [n^(2) + n-1] =(n)/(2) [2n ^(2) ] ]=n^(3) ` ` =(n)/(2) [n^(2) -n+1+ n^(2) + n-1])(n)/(2) [2n^(2) ] =n^(3)`. |
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