Middle Term

Middle Term

## Formula

If $$n$$ is even, there is one middle term:

$$T_{\frac n2+1}$$

Therefore:

$$T_{\text{middle}}={}^{n}C_{n/2}a^{n/2}b^{n/2}$$

If $$n$$ is odd, there are two middle terms:

$$T_{\frac{n+1}{2}}$$

and:

$$T_{\frac{n+3}{2}}$$

## Usage

- Used to find the middle term or middle terms without expanding the entire binomial.