Alternating Sum and Difference of Binomial Coefficients for Given n/Corollary

Corollary to Alternating Sum and Difference of Binomial Coefficients for Given n

$\ds \sum_{i \mathop \in \Z} \paren {-1}^i \binom n i = \delta_{n 0}$

Proof

From the definition of the binomial coefficient, when $i < 0$ and $i > n$ we have $\dbinom n i = 0$.

The result follows from Alternating Sum and Difference of Binomial Coefficients for Given n.

$\blacksquare$