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I would like to study the convergence of the series:

$$\sum_{n=1}^\infty \arctan \frac{1}{n^2}$$

but I don't know how to start.

please, can you make me understand how to solve it?

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  • 2
    $\begingroup$ $\arctan x\sim x$ as $x\to0$. $\endgroup$ – Lord Shark the Unknown Jan 14 '18 at 17:21
  • $\begingroup$ Compare it to a series that you know it converges. $\endgroup$ – Atmos Jan 14 '18 at 17:25
  • $\begingroup$ Probably compare to $\frac{1}{n^2}$ $\endgroup$ – valer Jan 14 '18 at 17:26
  • $\begingroup$ This question already has an answer here math.stackexchange.com/q/128357/269624 $\endgroup$ – Yuriy S Feb 7 '18 at 11:44

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