I'm trying to solve the following question: You and n other people (so n+1 people) each toss a probability-p coin, with $0\le P \le 1$. Then each person who got a head will split some arbitrary amount of prize money, K, equally. If nobody gets a head, then each person receives nothing. Whats the expected prize you receive? I think I want to first find the expected number of people who will toss heads, and in order to start I came up with the following summation:
$\sum{\frac{k}{x}(1-p)^{(n+1)-x}p^x}$, with $x$ from $1$ to $n+1$ where $n+1$ is the number of people.
However, I have no idea how to solve this sum, or even if I'm setting it up correctly (I think I may be missing something?); any tips would be greatly appreciated!