How to find the limit $\lim_{n\to \infty}\frac{n}{2^n-1}$? I've been trying to find and prove the 
$$\lim_{n\rightarrow\infty}\frac{n}{2^n-1}$$
but I haven't even figure out the limit, could anyone help?
$$\lim_{n\to\infty}\frac{n}{2^n-1}=\lim_{n\to\infty}\frac{1}{2^n\ln2}=\dfrac{1}{\ln{2}}\lim_{n\to\infty}2^{-n}=\dfrac{1}{\ln{2}}\cdot0=0$$
You can use Stolz theorem:

$ \lim \frac{a_n}{b_n}  = \lim\frac{a_{n+1}- a_n}{b_{n+1}-b_n} $

provided that $ b_n \rightarrow \infty $ monotonously