Approximation Using Binomial Theorem

Approximation Using Binomial Theorem

## Formula

For small $x$:

$$(1+x)^n\approx1+nx$$

For a more accurate approximation:

$$(1+x)^n\approx1+nx+\frac{n(n-1)}2x^2$$

## Conditions / Special Cases

The approximation is useful when:

$$|x|\ll1$$

## Usage

- Used to obtain quick approximations of powers and roots when the change from $1$ is small.