Relation Between Even and Odd Combinations

Rarely Tested

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.

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