Sum of Coefficients at Alternate Positions

Sum of Coefficients at Alternate Positions

## Formula

For:

$$(a+b)^n$$

the sum of coefficients corresponding to even powers of $$b$$ is:

$$\frac{(a+b)^n+(a-b)^n}{2}$$

The sum corresponding to odd powers of $$b$$ is:

$$\frac{(a+b)^n-(a-b)^n}{2}$$

## Usage

- Used to separate even and odd indexed terms of a binomial expansion.