So I'm back in grad school after a few years off. I'm trying to remember how to solve summation problems and it's eluding me. Hopefully you guys can help out.

I'm working with the quotient of some summations, trying to simplify into an overall equation. Here's what I'm looking at

1: Sum(X^b*e^(-a*X),X,1,n)

2: Sum(X^(b-1)*e^(-a*X),X,1,n)

3: Sum(X^(b+1)*e^(-a*X),X,1,n)

So the sum, with respect to X, from 1 to n, with a & b just adjustable parameters.

After I have the summations simplified, I will be dividing 1: by 2: and dividing 3: by 1:.

I think it has something to do with geometric or taylor series, but I just can't remember the operations.

Thanks in advance for the help.