Sum of series with binary parity in the numerator

I'm now stuck with this question, and I don't even know where to start: Find sum of series

$\sum _{1}^{\mathrm{\infty}}\frac{f(n)}{n(n+1)}$

, where f(n) - number of ones in binary representation of n.

I wish I could post some moves, that I've tried but I don't know what to do.

Thanks!

I'm now stuck with this question, and I don't even know where to start: Find sum of series

$\sum _{1}^{\mathrm{\infty}}\frac{f(n)}{n(n+1)}$

, where f(n) - number of ones in binary representation of n.

I wish I could post some moves, that I've tried but I don't know what to do.

Thanks!