The following is a problem from my probability practice final:
Let $X$ and $Y$ be discrete random variables with joint mass function
$f(x,y) = \frac{C}{(x+y-1)(x+y)(x+y+1)} $ for $x, y = 1, 2, 3...$
Calculate $C$ and find the marginal mass functions of $X$ and $Y$.
Now, to find the marginal distributions, I've tried to sum over all possible values of either variable (which is a sum that looks like it converges), but it's not a very pleasant task, and I can't find a way to do it nicely. Is there some shortcut here that I'm missing?