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$\arctan x\sim x$ as $x\to0$. – Angina Seng Jan 14 '18 at 17:21
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Compare it to a series that you know it converges. – Atmos Jan 14 '18 at 17:25
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Probably compare to $\frac{1}{n^2}$ – valer Jan 14 '18 at 17:26
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This question already has an answer here https://math.stackexchange.com/q/128357/269624 – Yuriy S Feb 07 '18 at 11:44