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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))+` . . . .
`z=(1)/(1^(2))-(1)/(2^(2))+(1)/(3^(2))-(1)/(4^(2))+` . . .then

A

`(x)/(1)=(4y)/(3),(4z)/(3)`

B

`(z)/(2),(x)/(3),(y)/(6)` 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, C
`y-x=3(x-z)`
`4x=3z+yimplies(y)/(6),(x)/(3),(z)/(2)` are in A.P.
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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

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