[tex]\sum_{n=1}^{\infty} \frac{o(2^n)}{2^n} = \frac{1}{9} [/tex](adsbygoogle = window.adsbygoogle || []).push({});

where [tex]o(2^n)[/tex] is the number of odd digits of [tex]2^n[/tex].

Found it in

http://mathworld.wolfram.com/DigitCount.html

equation (9)

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# How to calculate this sum?

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