# Limits of Sequences

Bashyboy

## Homework Statement

$\stackrel{lim}{n\rightarrow \infty} (-1)^n \frac{n}{n + 1}$

## 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.

Homework Helper
Gold Member

## Homework Statement

$\stackrel{lim}{n\rightarrow \infty} (-1)^n \frac{n}{n + 1}$

## 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.

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##?

Bashyboy
Ah, yes, I see. Thank you.

Staff Emeritus
\lim_{n\rightarrow \infty}