Answer
Convergent
Work Step by Step
Let $a_{n}=\frac{1}{(lnn)^{lnn}}$ and $b_{n}=\frac{1}{n^{2}}$
$\lim\limits_{n \to \infty}\frac{a_{n}}{b_{n}}=\lim\limits_{n \to \infty} \frac{n^{2}}{(lnn)^{lnn}}$
$=\lim\limits_{n \to \infty} \frac{e^{2lnn}}{e^{lnn}(lnln (n))}$
$=0$
The series is convergent.