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Sigma(r=1)^(infty) tan^(-1)(1)/(2r^(2))...

`Sigma_(r=1)^(infty) tan^(-1)(1)/(2r^(2))=t` then tan t is equal to

A

`2/3`

B

1

C

`sqrt(5)/(3)`

D

none of these

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AI Generated Solution

To solve the problem, we need to evaluate the infinite series given by: \[ t = \sum_{r=1}^{\infty} \tan^{-1}\left(\frac{1}{2r^2}\right) \] ### Step 1: Rewrite the series We can express the series in a different form: ...
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