Is there a closed form solution to the expression below? Or, if there is no closed form solution but the series converges, is there some upper bound on this expression?

$$\mathbb E_{i \sim Q}[i] = \sum_{i=k}^\infty i Q(i) = \sum_{i=k}^\infty i h {i \choose {k-1}} h^{k-1} (1-h)^{i - (k-1)}$$

The assumptions on constants $k$ and $h$ are that $k > 0$ and $0 < h < 1$. 

I'm out of my depth here, so any tips would be appreciated!

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P.S. This is my first question on MathOverflow. Let me know if you need more context, or if there's anything I can do to improve the question itself. 

  [1]: https://en.wikipedia.org/wiki/List_of_mathematical_series#Low-order_polylogarithms