Answer
Diverges
Work Step by Step
Consider $a_n=\lim\limits_{n \to \infty} \dfrac{\sqrt n}{\ln n}$
But $\lim\limits_{n \to \infty} \dfrac{\sqrt n}{\ln n}=\dfrac{\infty}{\infty}$
Need to apply L-Hospital's rule.
$\lim\limits_{n \to \infty} \dfrac{1/2 \sqrt n}{1/n} =\lim\limits_{n \to \infty} \dfrac{\sqrt n}{2}=\infty $
Hence, the given series diverges.
