यदि `1/1^2+1/2^2+1/3^2+1/4^2+...oo=pi^2/6`,

तब `1/2^2+1/4^2+1/6^2+1/8^2+...oo` का मान होगा

Options

A. `pi^2/12`
B. `pi^2/8`
C. `pi^2/24`
D. इनमे से कोई नहीं

Answer

C

Explanation

`S_1=1/1^2+1/2^2+1/3^2+1/4^2+...oo=pi^2/6`
माना `S_2=1/2^2+1/4^2+1/6^2+...oo`
`=1/2^2[1+1/2^2+1/4^2+1/6^2+...oo]`
`1/4*pi^2/6=pi^2/24`
`rArr" "S_2=pi^2/24`
`1/1^2+1/3^2+1/5^2==S_1-S_2=pi^2/8`