Waste less time on Facebook — follow Brilliant.

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
3 years, 3 months ago

No vote yet
3 votes


There are no comments in this discussion.


Problem Loading...

Note Loading...

Set Loading...