How do I take the limit as $n$ goes to $\infty$ of $\frac{\sqrt{n}}{\log(n)}$? How do take this limit:
$$ \lim_{n\to\infty} \frac{\sqrt{n}}{\log(n)}$$
I have a feeling that it is infinity, but I'm not sure how to prove it. Should I use L'Hopitals Rule?

Let $a(n) = \frac{\sqrt{n}}{\log(n)}$.
We want to show that $a(n)$ grows arbitrarily large.
$a(n^2) = \frac{n}{2\log(n)}$
so $\frac{a(n^2)}{a(n)} = \frac{\sqrt{n}}{2}$,
so, for $n >16$, $\frac{a(n^2)}{a(n)} > 2$.
Iterating or inducting or multiplying,
$\frac{a(n^{2^k})}{a(n)} > 2^k$,
so $a(n)$ gets arbitrarily large.
