# Thread: Series test for absolute/conditional convergence or divergence

1. ## Series test for absolute/conditional convergence or divergence

I've been stuck solving two questions:

1) (-1)^n all over(1 + 1/n)^n^2

I absolute valued the whole series to get rid of the (-1^n) and got stuck with something that seems almost like e on the bottom. But after applying the ratio test and a poor attempt to convert it into e, I got stuck.

2) (-1)^n * sin (1/n) all over ((ln(1+n))^2)

I'm not too sure on how to approach the problem. If I absolute value it and let the limit n tend to infinity, I get 0 over infinity.

Thank you for the help!

2. Hello,

For #1:
The absolute value of it is:

$\displaystyle \sum \dfrac{1}{\left( 1+\frac{1}{n} \right)^{n^2}}=\sum \left( \dfrac{1}{\left( 1+\frac{1}{n} \right)^{n}}\right)^n$

Try the Root Test.

For #2:
Try to use the comparison tests for it.

3. Sweet now I get the first question. Initially I did the same thing and thought that raising it to the n power would only result in n+1 for some odd reason.

But as for the second series, I used the comparison tests of two separate p series: 1/n and 1/n^2 and neither work. Mind hinting a bit more?