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Find the sum of infinite series s = si...

Find the sum of infinite series
`s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ((sqrt2 -1)/sqrt6) + sin ^(-1) ((sqrt3 - sqrt2)/(2sqrt3)) + ...+ sin^(-1) ((sqrtn - sqrt(n-1))/(sqrt(n(n+1))))+... infty`

A

`(pi)/(8)`

B

`(pi)/(4)`

C

`(pi)/(2)`

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
C
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