# a series with arctg

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?

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