Solving Limits of Sequences: (-1)^n \frac{n}{n + 1}

[Bashyboy]

Homework Statement

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

Homework Equations

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.

 

[LCKurtz]

Homework Statement

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

Homework Equations

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.

 

[micromass]

Writing limits in LaTeX looks better with the following code:

\lim_{n\rightarrow \infty}

There is no need for stackrel and such.