I need to prove that
$\log(n)/n\to 0$. Surely $\exists n\_0, \forall n > n\_0 \log(n) < n$. I want to give a general proof. That is:
for any sequence $a\_n \to \infty$ and $b\_n \to \infty, \exists n\_0, \forall n > n\_0: a\_n < b\_n \lim\_{n \to \infty} a\_n/b\_n = 0$.
Is it actually true? How can I prove it?