## How to calculate this sum?

$$\sum_{n=1}^{\infty} \frac{o(2^n)}{2^n} = \frac{1}{9}$$
where $$o(2^n)$$ is the number of odd digits of $$2^n$$.

Found it in
http://mathworld.wolfram.com/DigitCount.html
equation (9)
 Curses, JSTOR!

## How to calculate this sum?

 Quote by uart That's a pretty amazing series. I found some more information about it in the following paper. See : http://www.jstor.org/view/00029890/di991774/99p0626c/0
Fantastic! Thanks a lot!
Also found it in
Experimentation in Mathematics: Computational Paths to Discovery
By Jonathan M. Borwein, David H. Bailey, Roland
pag 14-15