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/proofoftheratiotest/proofoftheratiotest/
I'm trying to understand the proof, but there are some parts that I don't really get.
So assuming that a_{n+1}/a_{n} = L < 1
and that L < r
a_{n+1}/a_{n} < 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.
1. The problem statement, all variables and given/known data
http://blogs.ubc.ca/infiniteseriesmodule/appendices/proofoftheratiotest/proofoftheratiotest/
I'm trying to understand the proof, but there are some parts that I don't really get.
So assuming that a_{n+1}/a_{n} = L < 1
and that L < r
a_{n+1}/a_{n} < 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.