Sum of Even Index Binomial Coefficients

Theorem

 * $\displaystyle \sum_{i \mathop \ge 0} \binom n {2 i} = 2^{n-1}$

where $\displaystyle \binom n i$ is a binomial coefficient.

That is:
 * $\dbinom n 0 + \dbinom n 2 + \dbinom n 4 + \cdots = 2^{n-1}$