Prove that $\lim_\limits{n\to\infty }\frac{1}{\log(\log(n))}=0$ How to prove this limit?
$$\lim_{n\to\infty }\frac{1}{\log(\log(n))}=0$$
I thought of something like 
$$0 \le \frac{1}{\log(\log(n))} \le \frac{1}{n}$$
Is it alright?

Let $n=2^{2^k}$ and note that $\ln \ln x$ is monotonic
