I'm trying to make a small program, that gives me price distributions for tournaments and I thought using a series would be good for that.
I found this formula:
$$\sum_{k=1}^{n} a\ r^{k-1} = \frac{a(1-r^n)}{1-r}$$
Let's say I want the first price to get 50% and want to pay out places 1 through 8, then I'd have $n = 8$, $a = 1/2$. Is there a formula that would let me find the right r without having to solve for r every time?
Or what would be a better approach?
thank you