I'm sure this problem is obvious, but I don't know where to start.

Determine whether the series converges or diverges and give a good explanation how you arrived at your conclusion.

$\displaystyle \Sigma^{\infty}_{n = 1}n\sin{\frac{1}{n}}$

Also, for $\displaystyle \Sigma^{\infty}_{n = 1}\frac{1}{3 + n^2}$, I know I can use the integral test to show it converges, but can I also use the comparison test, comparing it to $\displaystyle \Sigma^{\infty}_{n = 1}\frac{1}{n^2}$?

Thanks in advance.