Condition for a Greatest Term

Condition for a Greatest Term

## Formula

If:

$$\frac{n-r}{r+1}\frac ba\le1$$

then $$T_{r+1}$$ is the greatest term, provided the preceding ratio is at least 1.

The greatest term occurs around:

$$r\approx\frac{nb-a}{a+b}$$

## Usage

- Used to locate the greatest term without calculating every term.