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

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

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

D

`n/(401 +20n)`

Text Solution

Verified by Experts

The correct Answer is:
C
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