Alternating Sum and Difference of Binomial Coefficients for Given n/Proof 2

Lemma
Let $n > 0$.

From the Binomial Theorem, we have that:


 * $\ds \forall n \in \Z_{\ge 0}: \paren {x + y}^n = \sum_{i \mathop = 0}^n \binom n i x^{n - i} y^i$

Putting $x = 1, y = -1$, we get: