Does the series (n/(ln n)^2) converge or diverege?

when i do the nth term test, it doesn't tell me anything
but when i do the limit comparison test, it diverges, why is this? Should the nth term test show divergence if the limit comparison test shows it?

Question

Does the series (n/(ln n)^2) converge or diverege?

when i do the nth term test, it doesn't tell me anything
but when i do the limit comparison test, it diverges, why is this? Should the nth term test show divergence if the limit comparison test shows it?

anonymous · Answer

Not all tests work for all series, which is one of the reasons there are so many tests.

The only way you'd really have a problem is if one test said it diverged and another said it converged.

anonymous · Answer

if $ \displaystyle \lim_{n \rightarrow +\infty} u_n \neq 0$ then $\displaystyle \sum_{n=1}^{+\infty} u_n$ is divergent