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If S= tan^-1 (1/(n^2+n+1))+tan^-1 (1/(n^...

If `S= tan^-1 (1/(n^2+n+1))+tan^-1 (1/(n^2+3n+3))+…+tan^-1 (1/(1+(n+19)(n+20)))` then tan S is equal to` (A) `20/(401+20n)` (B) `n/(n^2+20n+1)` (C) `n(401+20n)` (D) `20/(n^2+n-1)`

A

`20/(401+20n)`

B

`n/(n^2+20n+1)`

C

`20/(n^2+20n+1)`

D

`n/(401+20n)`

Text Solution

Verified by Experts

The correct Answer is:
C
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