Pre-Exam Calculus Questions

I will be glad to get some guidance to the following questions:

1. Determine whether the next series converges , diverges or absolutely converges:

$\displaystyle \Sigma_{n=2}^{\infty} \frac{(-1)^{n}}{ln(n)} (\frac{1}{2} + \frac{2}{2^{2}} +...+\frac{n}{2^{n}} ) $ .

2. Find all the values of the parameters a,b which for these values the integral converges:

$\displaystyle \int_{0}^{\infty} \frac{arctan(x^{2})}{\sqrt{x^{a}+x^{b}}} $ .

Thanks in advance... I'll show what I've tried in the reply.