calculus - Find the infinite sum $sum_{n=1}^{infty}frac{1}{2^n-1}$

How to evaluate this infinite sum?

$$\sum_{n=1}^{\infty}\frac{1}{2^n-1}$$

Answer

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.