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If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/...

If `1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^2)+` equals `pi^2//8` b. `pi^2//12` c. `pi^2//3` d. `pi^2//2`

A

`pi^2//8`

B

`pi^2//8`

C

`pi//3`

D

`pi^2//2`

Text Solution

Verified by Experts

The correct Answer is:
A
`1/1^(2)+1/3^(2)+1/5^(2)+1/7^(2)+..`
`=(1/1^(2)+1/2^(2)+1/3^(2)+1/4^(2)+1/5^(2)+1/6^(2)+1/7^(2)+..)`
`-(1/2^(2)+1/4^(2)+1/6^(2)+..)`
`=pi^(2)/6-1/4(1/1^(2)+1/2^(2)+1/3^(2)+..)`
`=pi^(2)/6-1/4(pi^(2)/6)`
`=pi^(2)/8`
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