# Thread: Does this series converge or diverge

1. ## Does this series converge or diverge

Ok, I have another series im puzzled on how to approach. In my calc 3 class, we learned how to apply the divergence and integral tests but im not sure which to use. the series is Tan-1 K / 1+ K^2.

Thanks for any help or suggestions!

2. You can just bound the general term, since $-\frac{\pi }{2}<\arctan x<\frac{\pi }{2}$ holds for all $x\in\mathbb R.$

3. $\sum\limits_k {\frac{{\arctan (k)}}
{{1 + k^2 }}} \leqslant \frac{\pi }
{2}\sum\limits_k {\frac{1}
{{1 + k^2 }}}
$