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Find the sum to n terms of the series S...

Find the sum to n terms of the series `S_(n)=cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^(3)+(1)/(2^(2)))+cot^(-1)(2^(4)+(1)/(2^(3)))+.....` upto n terms ?

A

`tan^(-1)(2^(n))-tan^(-1)(2)`

B

`tan^(-1)(2^(n+1))-tan^(-1)(2)`

C

`tan^(-1)(2^(2n))-tan^(-1)(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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