Does this series converge or diverge? $\sum_{n=1}^\infty\ln\left(1+\frac1{n^2}\right)$ I have a series here, and I'm supposed to determine whether it converges or diverges. I've tried the different tests, but I can't quite get the answer.

$$\sum_{n=1}^\infty\ln\left(1+\frac1{n^2}\right)$$


Hint: Recall that $\ln(1+x)\sim x$ for $x\to 0$, and use the fact that $\sum_{n=1}^\infty\frac1{n^2}$ is convergent.
