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sum(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))...

`sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1))))` is equal to

A

`tan^(-1)(sqrt(n))-(pi)/4`

B

`tan^(-1)(sqrt(n)+1)-(pi)/4`

C

`tan^(-1)(sqrt(n))`

D

`tan^(-1)(sqrt(n)+1)`

Text Solution

Verified by Experts

The correct Answer is:
C
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