Help finding the output for input with conditions
So since since my system is causal I obtain, $y[k] = e^{2\pi i ks_0}\sum_{n=0}^{\infty}h[n]e^{-2\pi i ns_0}$.  From here I can conclude that since the system is stable this series converges, but without knowing more information about $h[n]$ I can't see any way to further simplify the expression and rid myself of this infinite sum.  


Hint:  The function (of $z$) defined by $\sum_n h[n]z^{-n}$ is given a special
name and is of some importance in signal-processing circles. Do you know about
this function?
What is the value of this function at $z = e^{2 \pi i s_0}$? which by the way
lies on the unit circle in the complex plane, seeing as how we are talking of circles.