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)`.

Explanation

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)`.