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