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If 1/1^2 + 1/2^2 + 1/3^2 + ........ upto infinity = pi^/6, then 1/1^2 + 1/3^2 + 1/5^2 +..... =

If 1/1^2 + 1/2^2 + 1/3^2 + ........ upto infinity = pi^/6, then 1/1^2 + 1/3^2 + 1/5^2 +..... =

Grade:11

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
1/1^2 + 1/2^2 + 1/3^2 + ........ upto infinity = pi^n ...(1)...(n=1/6 or whatever, not mentioned in the question)

Let [1/1^2 + 1/3^2 + 1/5^2 + ........ upto infinity]= So ...(2)
(1)-(2)=1/2^2 + 1/4^2 + 1/6^2 + ........ upto infinity = pi^n – So
=(1/22)[1/1^2 + 1/2^2 + 1/3^2 + ........ upto infinity ]=pi^n – So
=(1/22)[pi^n]=pi^n-So
Solve the equation to get the value of Soin terms of pi^6

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