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The sum tan^(-1).(1)/(1+x+x^2)+tan^(-1)....

The sum `tan^(-1).(1)/(1+x+x^2)+tan^(-1).(1/(3+3x+x^2))+tan^(-1).(1/(7+5x+x^2))+tan^(-1)(1/(13+7x+x^2))` of first 100 terms of the series is

A

`tan^(-1) (100/(1+x^2+100x))`

B

`tan^(-1)((2x-100)/(1-x^2-100x))`

C

`tan^(-1)(100/(1+x^2-100x))`

D

`tan^(-1)((2x+100)/(1+x^2-100x))`

Text Solution

Verified by Experts

The correct Answer is:
A
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