Pascal's Rule/Real Numbers

Theorem
Let $\displaystyle \binom r k$ be a binomial coefficient.

Then:
 * $\displaystyle \forall r \in \R, k \in \Z: \binom r {k-1} + \binom r k = \binom {r+1} k$

Proof
From Factors of Binomial Coefficients:

Dividing by $\left({r + 1}\right)$ yields the solution.