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The sum of the series to infinity cot^(...

The sum of the series to infinity `cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^(3)+(1)/(2^(2)))+cot^(-1)(2^(4)+(1)/(2^(3))).... oo=cot^(-1)(k)`, then the value of k is___________.

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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VMC MODULES ENGLISH-INVERSE TRIGONOMETRY-LEVEL-2
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