$0<p<1$
$\sum_{k=1}^{\infty} k (1 - p)^{k-1}$
How'd I go by calculating this?
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1The formula for $\sum_k kx^k$ and the likes of it has been asked a considerable number of dozens of times on this site. Search for it. – May 22 '17 at 16:09
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You know that $\sum_{k=0}^\infty(1-p)^{k}=\frac{1}{p}$. Consider differentiating both sides in $p$. – Alex R. May 22 '17 at 16:10