Answer
Converges
Work Step by Step
Let us consider $u_n=\dfrac{1}{\ln n}$ and $u_n$ refers to the all positive values of $n$.
The given function implies that $\ln n$ is an increasing function, but the sequence $u_n$ is decreasing.
Then, $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \dfrac{1}{\ln n}=0$
Hence, the series converges by the Alternating Series Test.
