Hello, I have a question:

$\displaystyle \sum_{n=1}^{\infty} \ln (1+\frac{x^2}{n\ln^2(n)}), x \in (-a,a)$

Does it converge? If so, does it uniformly converge?

Thought of turning the ln into two different ln's, but I really can't find a way to prove a convergence of anything here...

Can you please help me?

Thanks :)