# Homework Help: Defintion of e as a limit

1. Sep 18, 2009

### blerg

1. The problem statement, all variables and given/known data
Show that $$x_n = \left(1 + \frac{1}{n}\right)^{n+1}$$ is decreasing and bounded below

2. Relevant equations

3. The attempt at a solution
I have tried all sorts of things and none some to be working. I tried expanding it using the binomial theorem, but there are more terms in $$x_{n+1}$$ than $$x_n$$ so i didn't see an easy way to compare them. I tried looking at $$\frac{x_{n+1}}{x_n}$$ and $$x_nx_{n+1}$$ with nothings giving me and progress. Any suggestions?