Alternating Sum and Difference of Binomial Coefficients for Given n/Corollary
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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.
$\blacksquare$