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If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then...

If `1-1/3+1/5-1/7+1/9-1/(11)+=pi/4` , then value of `1/(1xx3)+1/(5xx7)+1/(9xx11)+` is `pi//8` b. `pi//6` c. `pi//4` d. `pi//36`

A

`pi//8`

B

`pi//6`

C

`pi//4`

D

`pi//36`

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`pi/4=(1-1/3)+(1/5-1/7)+(1/9-1/11)+…`
`=2/(1xx3)+2/(5xx7)+2/(9xx11)+..`
`rArr1/(1xx3)+1/(5xx7)+1/(9xx11)+..=pi/8`
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