Series test for convergence/divergence

[Benjer]

Hi Parisse,

I see that the value of the main term is n^(-3/2) but I don't know the connection between that and whether the series converges or diverges. I guess what I'm asking is, if I apply the series command to some function, what am I looking for in the output to see if the series converges or diverges? I tried some different series that I know are convergent and divergent, but I couldn't see a pattern in the output that helped me connect the two.

Thank you for your time.