I've been teaching myself Calc. BC this year for the AP test, and this test for infinite series I've proved to be useful in analyzing these things, but I'm not sure how it was derived. I think I'm missing something simple, as the proof in my book is very short, but for this same reason maybe I haven't totally grasped it yet. My Calculus teacher hates infinite series (for whatever reasons) and therefore wasn't much help. Could someone try to break it down for me? Thanks in advance.

If An and Bn are both greater than zero

(lim n->infinity (An/Bn))>0

Then both series converge or diverge.