Answer
Diverges
Work Step by Step
Consider $a_n=\dfrac{\ln n}{n}$
Since, we know that $\ln n \geq 1$ for the all value of $n$.
Thus, $\Sigma_{n=1}^\infty \dfrac{\ln n}{n} \geq \Sigma_{n=1}^\infty \dfrac{1}{n}$
we see that the series $\Sigma_{n=1}^\infty \dfrac{1}{n}$ is a divergent harmonic series.
Hence, the given series Diverges by the direct comparison test.