Prove that for every natural numbern, we can express nk, wherek≥ 2 is an integer, as a sum of n consective odd natural numbers.

Dear Ajinkya,

you have to prove that 

1+3+5+7+ -------- +n  = n^k   ;while k>= 2.

Therefore : 1+3+5+7 ----------+ n  = [2a +(n-1)d]n/2 ; a= first term; d = common difference.

put the value in the formulae

thus   1+3+5+7+ ------------+ n = [2*1 +(n-1)*2]n/2 = n²   which is true for k>= 2 

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