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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.

8 years ago

Answers : (1)

Radhika Batra
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 provides online iit jee courses and IIT JEE Test Series with IITians. Click here to get free online test series and check your status timely or you can join us as our registered user for getting best iit jee study material or iit jee test series.

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thanks and regards.

Akhilesh Shukla

8 years ago
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