Wikipedia gives an interesting infinite sum for Euler's constant $\gamma$ and I was wondering how one would evaluate this interesting sum. The sum is given as follows:
Let $N_0 (x)$ and $N_1 (x)$ represent the number of zeros (OEIS A023416) and ones (OEIS A000120) respectively of the binary expansion of $n$.
$ \sum_{n=1}^\infty \frac{N_1(n) + N_0(n)}{2n(2n+1)} = \gamma $