change for $1 using generating functions Using only pennies and dimes, how many ways can you make change for $1 using generating functions.
I came up with the equation $(1+x^2+x^3+\ldots)(1+x^{10}+x^{20}+\ldots)$
which simplifies to $\frac{1}{1-x^1}\frac{1}{1-x^{10}}$.
I assume I need to find the coefficient at $x^{100}$ because it's $100$ cents, but I'm not sure where to go from here.

You can just read it off via: $x^{10}x^{90}+x^{20}x^{80}+\ldots$. So it amounts to figuring out how many terms you have. 
