Hi everyone, I'm currently taking Calc II course and I'm kind of stuck in this ratio test proof thing. 1. The problem statement, all variables and given/known data http://blogs.ubc.ca/infiniteseriesmodule/appendices/proof-of-the-ratio-test/proof-of-the-ratio-test/ I'm trying to understand the proof, but there are some parts that I don't really get. So assuming that |an+1/an| = L < 1 and that L < r |an+1/an| < r but then, the proof says there is an integer N which is < or = to n. From where did that come from? Why do we need it in the first place? And how does it relate to the proof? The proof goes on and I don't really have any idea what's going on. 2. Relevant equations - 3. The attempt at a solution I tried making a number line to understand what's going on but this seems so subtle.