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ajinkya bhole Grade: 10

Prove that for every natural number

n, we can express nk, where k≥ 2 is an integer, as a sum of n consective odd natural numbers.

7 years ago

## Answers : (1)

247 Points

Dear Ajinkya,

you have to prove that

1+3+5+7+ -------- +n  = nk   ;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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thanks and regards.

Akhilesh Shukla

7 years ago
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