I want to choose n balls from 2 types using generating functions.
Normally I would think to write $f(x)=(1+x+...+x^n)^2 = \left ( \frac{1-x^{n+1}}{1-x} \right )^2$ and then look for the coefficient of $x^n$, but I'm thinking that since any coefficient after $x^n$ won't contribute anything I should be able to use the simpler expression $(1+x+...)^2 = \left ( \frac{1}{1-x} \right )^2$ Is this correct? Is it something I would need to prove or is the simple explanation above sufficient?