# Homework Help: Limit Proof

1. Nov 12, 2009

### tarheelborn

1. The problem statement, all variables and given/known data

How do I prove that lim 2^(1/n) = 1?

2. Relevant equations

3. The attempt at a solution

2. Nov 12, 2009

### foxjwill

What have you done so far?

3. Nov 12, 2009

### tarheelborn

This is actually part of a series problem, so I have determined that the sequence of a_n's is decreasing and that it seems to converge to 1. I know that I need to find N \in the naturals such that |2^(1/n)| < epsilon, but I can't seem to figure out how to solve in terms of epsilon.

4. Nov 12, 2009

### foxjwill

Since $2^{1/n}$ is always greater than 1 (prove this!), you can forget the absolute value. Try taking the natural log of both sides of $2^{1/n}-1<\epsilon$ and solving for $n$.