Sum of Even-Power Coefficients

Sum of Even-Power Coefficients

## Formula

If:

$$P(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n$$

then the sum of coefficients of even powers is:

$$\frac{P(1)+P(-1)}2$$

For:

$$P(x)=(1+x)^n$$

this becomes:

$$2^{n-1}$$

for:

$$n\ge1$$

## Usage

- Used to find the sum of coefficients corresponding to even powers without expanding the binomial.