Answer
Converges
Work Step by Step
Apply the limit comparison test.
Therefore, $ \lim\limits_{k \to \infty} \dfrac{a_k}{b_k}=\lim\limits_{k \to \infty} \dfrac{\tan^{-1} k/k^2}{1/k^2}\\=\lim\limits_{k \to \infty} \arctan (k) \\=\dfrac{\pi}{2}$
So, we can conclude that the given series converges by the limit comparison test.