Hello,

I am having trouble finding out if the following two series converge.

a) $\displaystyle \sum_{n=1}^{+\infty}{\frac{n+1}{\sqrt{n}+1}\sin{\f rac{1}{n^2}}}$

b) $\displaystyle \sum_{n=1}^{+\infty}{\log\left({1+\frac{1}{n^2}}\r ight)}$

Any help would be appreciated.