- #1

saybrook1

- 101

- 4

## Homework Statement

I would like to understand how the limit was changed in the ratio test from step 1 to step 2 in the image that I've posted. I thought that the denominator would look like (2/n+2)(2/n+1) in step 2 since it looks like we are just turning the n's into reciprocals. Any help here would be greatly appreciated. Thank you very much as always.

## Homework Equations

Power series, limits, reciprocals.

## The Attempt at a Solution

I've tried to figure out why the argument in the second set of parentheses in the denominator becomes (2+1/n) instead of (2/n+1) once the limit is changed from infinity to zero in between steps 1 and 2. Just with brute force algebra I couldn't figure out how they went from step 1 to 2.