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

2. Find all the values of the parameters a,b which for these values the integral converges:
$\int_{0}^{\infty} \frac{arctan(x^{2})}{\sqrt{x^{a}+x^{b}}}$ .

2. ## ...

If we take this series from n=3 in absolute value, we can say it's less than:
$\Sigma_{n=2}^{\infty} (\frac{1}{2}+...+\frac{n}{2^{n}} )$
All I need is to show that the series above converges...The problem is that the number of conjunct elements depends on n...

The second one:
The only problematic point is 0 ... We can substitute $x^{2}= t$ or something, but I don't think it's necessary ... Because we can say it's less than $\frac{\pi}{2} \frac{1}{\sqrt{x^{a}+x^{b}}}$... I can't figure out how to use now something like the comparison test... There must be an easy way...

About the third one- I've no idea

Thanks a lot!