Limit at infinity

[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

[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?

[IniquiTrance]

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

[w3390]

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

[IniquiTrance]

Right. Thanks guys!