Find the infinite sum $\sum_{n=1}^{\infty}\frac{1}{2^n-1}$
How to evaluate this infinite sum? $$\sum_{n=1}^{\infty}\frac{1}{2^n-1}$$
Yes. I found it. It is called the Erdős-Borwein Constant.
$$E=\sum_{n\in Z^+}\frac{1}{2^n-1}$$
Check http://mathworld.wolfram.com/Erdos-BorweinConstant.html
According to the page, Erdős showed that it is irrational.
I think you wanna see this:
Ramanujan’s Notebooks Part I
Click me and try Entry $14$ (ii) / pag 146 where you set $x=\ln2$
Chris.