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!