How do you prove $\lim_{n\to\infty} 1/n^{1/n}$ using only basic limit theorems? How do you prove $\lim_{n\to\infty} \frac {1}{n^{1/n}}$ using only basic limit theorems? I thought it was $0$, but my book lists the solution as $1$. How come?

Hint: Use $ \lim_{n\to \infty} (a_n)^{1/n}=l $ if $\lim_{n\to \infty}\frac{a_{n+1}}{a_n}=l$
