Greatest Term in a Binomial Expansion

Greatest Term in a Binomial Expansion

## Formula

For:

$$(a+b)^n$$

with $a,b>0$, the ratio of consecutive terms is:

$$\frac{T_{r+2}}{T_{r+1}}=\frac{n-r}{r+1}\frac ba$$

The terms increase while:

$$\frac{n-r}{r+1}\frac ba>1$$

and decrease when:

$$\frac{n-r}{r+1}\frac ba<1$$

## Usage

- Used to determine the greatest term of a binomial expansion.