Question

does the series n/(ln(n))^2 converge or diverge?

Answer 1

Looking at the summand:
\( \dfrac{n}{\left( \ln n \right)^2} \)
This is immediately divergent at n=1, but if we assume it isn't relevant, we should test the limit as n approaches infinity of the summand. Have you tried this already?

Answer 2

\( \displaystyle \lim_{n \to \infty} \left( \dfrac{n}{\left( \ln n \right)^2} \right) \)