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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Closed formula for series $\sum_{i=1}^{\infty} \frac{1}{x^i-y^i}$

What can be said about $\sum_{i=1}^{\infty} \frac{1}{x^i-y^i}$ (for $|x|>1$ and $|y|>1$ and $x\neq y$)? Is there a kind of closed formula for this? By comparing to the geometric series, this sum shoul …