Sums of digits and the Hurwitz zeta function

@inproceedings{Allouche1990SumsOD,
  title={Sums of digits and the Hurwitz zeta function},
  author={Jean-Paul Allouche and Jeffrey Shallit},
  year={1990}
}
  • Jean-Paul Allouche, Jeffrey Shallit
  • Published 1990
  • Mathematics
  • Let s2(n) denote the sum of the binary digits of n. Then it is easily seen that $$\sum\limits_{n = 1}^{ + \infty } {\frac{{s_2 (n)}}{{n(n + 1)}} = 2Log2.}$$ 

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