1) . You can apply the integral test, or recognize that it's a p-series, where (thus, the series converges).

2) . Again apply the integral test, or recognize it's a p-series, where (thus, the series diverges).

3) I forget how to prove it, but it diverges. (expanding we get 3-3+3-3+3-3+...)

4) . I believe you would use the limit comparison test here (?) : Thus, . Since this doesn't exist, then the series diverges. (I think this is correct)

5) . I'm sure the integral test would work here as well. It's pretty evident that the series diverges.

Can someone verify these??