# Choosing n balls from 2 types

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?

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This is part of a larger 1st year undergrad assignment. Do you think stating that since the coefficients greater than $x^n$ don't contribute they can be ignored and the simpler expression can thus be used would be a sufficient explanation? –  Robert S. Barnes Jan 20 '12 at 11:38