# Limit at infinity

1. Oct 20, 2009

### IniquiTrance

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

How can I prove that:

$$\lim_{n \rightarrow \infty} n^{\frac{1}{n}}=1$$

Isn't $$\infty^{0}$$ indeterminate?
Thanks!

2. Relevant equations

3. The attempt at a solution

2. Oct 20, 2009

### Dick

Yes, it is indeterminant. That's not the end of the story. Indeterminant just means you don't know what the limit is yet. Take the log. Can you prove (1/n)*log(n) approaches 0?

3. Oct 20, 2009

### IniquiTrance

That becomes $$0*\infty$$, isn't that indeterminate as well?

4. Oct 20, 2009

### w3390

Can't you use L'Hopital's rule?

5. Oct 20, 2009

### IniquiTrance

Right. Thanks guys!