How do I solve the following equation for $f(\cdot)$?


$f(x)+\frac{1}{n}f(nx)=\sin(x)$


That is, how do I create a function which, when combined with its nth harmonic, will be a sine wave?



How to create a function whose harmonic is a sine wave
$$\sum\_{k=1}^\infty (\frac{-1}{n})^{k-1}\sin(n^kx)$$


