Relation Between Even and Odd Combinations
## Formula
$$\sum_{\substack{r=0\\r\text{ even}}}^{n}{}^nC_r=\sum_{\substack{r=0\\r\text{ odd}}}^{n}{}^nC_r=2^{n-1}$$
for:
$$n\ge1$$
## Usage
- Used when a problem separates binomial coefficients according to even and odd indices.