I have a few series which I'm having trouble proving whether they converge or diverge. I know the following tests for convergence: comparison test, ratio test, n-th term test, and root test. Here are the series and what I have tried so far:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum[/tex] n -1 / n^{2}: I'm assuming this series diverges, since it behaves like 1/n, which also diverges. I'm trying to use the comparison test to see if I can find a "smaller" series which also diverges, but coming up blank. I tried the ratio test to no avail, since it gives 1.

[tex]\sum_{n=2}^\infty[/tex] 1 / (n + (-1)^{n})^{2}: I'm really not sure where to begin with this one. The (-1)^{n}is really throwing me off. I'm assuming this converges.

And finally,

[tex]\sum[/tex] n! / n^{n}: I tried the ratio test, canceling out the factorial and getting the ratio of n^{n}/ (n + 1)^{n}. This limit seems to be 1, so the ratio test doesn't really help me here. Any suggestions?

Thanks for any help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Series - Testing for Convergence / Divergence

**Physics Forums | Science Articles, Homework Help, Discussion**