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?