Answer
the series diverges
Work Step by Step
nth term test of divergence:
if $\lim\limits_{n \to \infty} {a_{n}} \ne 0$, then the series $\Sigma a_{n}$ diverges.
In the problem $a_{n} = arctan(n)$
$\lim\limits_{n \to \infty} arctan(n) = \frac{\pi}{2}$
Since $ \frac{\pi}{2} \ne 0$, the series $\sum_{n}^{\infty} \arctan n $ diverges.
