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sum(n=1)^oo(tan^-1((4n)/(n^4-2n^2+2))) i...

`sum_(n=1)^oo(tan^-1((4n)/(n^4-2n^2+2)))` is equal to (A) `tan ^-1 (2)+tan^-1 (3)` (B) `4tan^-1 (1)` (C) `pi/2` (D) `sec^-1(-sqrt2)`

A

`tan^(-1). 1/2 + tan^(-1). 2/3`

B

`4 tan^(-1) 1`

C

`pi/2`

D

`sec^(-1) ( - sqrt2)`

Text Solution

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The correct Answer is:
A
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