# Limits of Sequences

1. Sep 27, 2012

### Bashyboy

1. The problem statement, all variables and given/known data
$\stackrel{lim}{n\rightarrow \infty} (-1)^n \frac{n}{n + 1}$

2. Relevant equations

3. The attempt at a solution
The answer is that the limit oscillates between -1 and 1, but I was wondering if there was an analytic was of showing this.

2. Sep 27, 2012

### LCKurtz

Well, you know the sign alternates. What happens if you divide the numerator and denominator of your fraction by n? What happens then as $n\to\infty$?

3. Sep 27, 2012

### Bashyboy

Ah, yes, I see. Thank you.

4. Sep 27, 2012

### micromass

Staff Emeritus
Writing limits in LaTeX looks better with the following code:

Code (Text):

\lim_{n\rightarrow \infty}

There is no need for stackrel and such.