# Prove the following power series solution

Prove the following power series equality:

$$\sum_{n\geq0} {n \choose k-1} x^{n} = x^{k-1}/(1-x)^k$$

I'm not sure if I am on the right track, but I tried answering this through induction on k. With base case k = 1. I got $$\sum_{n>=0}x^{n} = (1-x)^{-1}$$ which holds. When I try for m + 1 I get $$x^{m}/((1-x)^m(1-x))$$ but im not sure how to continue from here. I was thinking of writing the bottom half of the fraction as a sum, but I'm not sure what I would do with the x^m term

• – D Poole Sep 30 '16 at 12:40
