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Proof of formula for expansion

I was working with generating functions on the Dice Rolls problem in last week's Comp. Sci. problem set and stumbled because I could not find this equation:

$$\frac {1}{(1-x)^n} = \displaystyle \sum_{i = 0}^{\infty} {n+i-1 \choose i} x^i$$

Is there a way to prove that the coefficient for this expression is correct using the binomial theorem (or the generalized version) and some binomial coefficient identities?

Note by Sebastian Garrido
4 years, 8 months ago

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