Negated Upper Index of Binomial Coefficient/Corollary 1/Proof 2

Corollary to Negated Upper Index of Binomial Coefficient
Let $r \in \R, k \in \Z$.

Then:
 * $\displaystyle \binom {-r} k = \left({-1}\right)^k \binom {r + k - 1} k$

where $\displaystyle \binom {-r} k$ is a binomial coefficient.