Limit comparison
For two series, A and B, if A > 0 and B > 0, and lim (A/B) = L, where L is finite and POSITIVE, then either both series converge or diverge.
In laymans, take a benchmark of a term that you know to converge or diverge, and compare it to your function in question. They have to be somehow related though, otherwise that's just silly.
IF THE LIMIT IS 0, you learn NOTHING and must try another test!