Could somebody check if this is correct?
$$\lim_{n \to \infty} \frac {\log_{2}(\log_{2}(n))}{\log_{2}(n)}$$
I exponantiate the numerator and the denominator with 2
$$\frac {(\log_{2}(\log_{2}(n)))^2}{(\log_{2}(n))^2}$$
$$ = \frac {\log_{2}(n)}{n}$$
I extract the constant from the logarithm
$$ = \log_{2}(e) * \lim_{n \to \infty} \frac {\ln(n)}{n}$$
Using de l'Hospital:
$$ = \log_{2}(e) * \lim_{n \to \infty} \frac {\frac {1}{n}}{1}$$
$$ = \log_{2}(e) * \lim_{n \to \infty} \frac {1}{n} = 0$$
Is that correct?