Generalized Binomial Theorem

Generalized Binomial Theorem

## Formula

For any real number $$n$$:

$$(1+x)^n=1+nx+\frac{n(n-1)}{2!}x^2+\frac{n(n-1)(n-2)}{3!}x^3+\cdots$$

For:

$$|x|<1$$

the general term is:

$$T_{r+1}=\frac{n(n-1)\cdots(n-r+1)}{r!}x^r$$

## Usage

- Used to expand binomials having non-positive or non-integral powers.