Hello,

I have two problems with series first $\displaystyle \sum^{\infty }_{n=1}\frac{(-1)^nn^2}{n^3+1}$

so I will like to know of this is absolute convergent here for I use two test.

First $\displaystyle \frac{n^2}{n^3+1} =^?0$ and I think this is oké $\displaystyle \frac{n^2(1)}{n^2(n+\frac{1}{n^2})}= \frac{1}{n+ \frac{1}{n^2}}=0$

then the second test $\displaystyle \frac{n^2}{n^3+1}<\frac{(n+1)^2}{(n+1)^3+1}$ but the dominator will be bigger then te nominator?

Or not?

Second problem $\displaystyle \sum^{\propto}_{n=1}\frac{n}{2n+1}$

I will proof that this is convergent $\displaystyle \frac{\frac{(n+1)}{2n+3}}{\frac{n}{2n+1}}=\frac{n+ 1}{2n+3}\frac{2n+1}{n}$

if I calculated this then I get $\displaystyle \frac{5}{2}$ thus not convergent but it must be.

Who can help me out? Greets.