I am currently trying to find when series converge or diverge. I am learning this form a text with very little input from a prof (online classes) It seems that there is alot of personal technique in determining convergence. The book gives a few theorems, which I understand. But knowing which function to choose for comparison and manipulation inorder to use these theorems is not explained in the text. From looking at the study guide it appears there are multiple ways to arrive at the answer, and it may have to do with personal preference.

So my question is this. What are your steps that you like to use to determine conv./diver. Multiple answers would be welcome as it seems this might have some basis in personal choice.