The standard normal distribution given here by $F$, satisfies the following limit:
$$ n(1-F(a_n x+b_n)) \rightarrow e^{-x} \;\;\text{ as }\;\; n \rightarrow \infty$$
with
$$b_n=(2\log(n)+\log(\log(n))+\log(4\pi))^{1/2}$$
and
$$a_n=\frac{1}{b_n}$$
How do I show that?
By using the fact that $\frac{b_n}{\sqrt{2\log(n)}}$ converges to $1$, I can transform the brackets to: $F(\frac{x+ \log n}{\sqrt{2 \log n}})$
My problem now is that I don´t know how to proceed.