Answer
Diverges
Work Step by Step
Consider $a_n=\dfrac{1}{\ln n}$ and $b_n=\dfrac{1}{n}$
Now, $\lim\limits_{n \to \infty}\dfrac{a_n}{b_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{1}{\ln n}}{\dfrac{1}{n}}$
Thus, we have $ =\lim\limits_{n \to \infty} \dfrac{n}{\ln n}$
or, $=\infty$
Hence, the series is divergent due to the limit comparison test.
