Answer
Diverges
Work Step by Step
Let $u_n=\dfrac{1}{\ln n}$ and $v_n=\dfrac{1}{n}$
Now, $\lim\limits_{n \to \infty}\dfrac{u_n}{v_n} =\lim\limits_{n \to \infty}\dfrac{1/\ln n}{1/n}$
$\implies \lim\limits_{n \to \infty} \dfrac{n}{\ln n}=\dfrac{\infty}{\infty}=\infty$
Thus, the series diverges due to the limit comparison test.