Answer
Divergent
Work Step by Step
$\lim\limits_{n \to \infty}\frac{a_{n}}{b_{n}}=\lim\limits_{n \to \infty}\frac{tan(1/n)}{1/n}$
Note that $\Sigma_{n=1}^{\infty}\frac{1}{n}$ is a harmonic series, which is divergent.
The series is divergent.