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If x=(1)/(1^(2))+(1)/(3^(2))+(1)/(5^(2))...

If `x=(1)/(1^(2))+(1)/(3^(2))+(1)/(5^(2))+....` , `y=(1)/(1^(2))+(3)/(2^(2))+(1)/(3^(2))+(3)/(4^(2))+....` and `z=(1)/(1^(2))-(1)/(2^(2))+(1)/(3^(2))-(1)/(4^(2))+...` then

A

`x`, `y`,`z` are in `A.P.`

B

`(y)/(6)`, `(x)/(3)`,`(z)/(2)` are in `A.P.`

C

`(y)/(6)`, `(x)/(3)`,`(z)/(2)` are in `A.P.`

D

`6y`, `3x`, `2z` are in `H.P.`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `y-x=3((1)/(2^(2))+(1)/(4^(2))+(1)/(6^(2))+…)`
`x-z=((1)/(2^(2))+(1)/(4^(2))+(1)/(6^(2))+…)`
`:. (y-x)=3(x-z)`
`implies4x=y+3zimplies2(x)/(3)=(y)/(6)+(z)/(2)`
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