Answer
Diverges
Work Step by Step
Consider $a_n=\dfrac{\ln n}{\ln (\ln n)}$
Now, $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \dfrac{\ln n}{\ln (\ln n)}$
Here, $\lim\limits_{n \to \infty} \dfrac{\ln n}{\ln (\ln n)}=\dfrac{\infty}{\infty}$
This shows an Inderminate form of a limit, so apply L'Hospital's rule such that $\lim\limits_{x \to l}\dfrac{a(x)}{b(x)}=\lim\limits_{x \to l}\dfrac{a'(x)}{b'(x)}$
Thus,
$\lim\limits_{n \to \infty}\dfrac{n \ln n}{n}=\infty$
Thus, the series Diverges.
