Alternating Sum and Difference of Binomial Coefficients for Given n

Theorem

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

where:
 * $\dbinom n i$ is a binomial coefficient
 * $\delta_{n 0}$ denotes the Kronecker delta.