Expansion of $$(1+x)^{-n}$$

Expansion of $$(1+x)^{-n}$$

## Formula

For positive integer $$n$$:

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

For:

$$|x|<1$$

the general term is:

$$T_{r+1}=(-1)^r{}^{n+r-1}C_rx^r$$

## Usage

- Used for binomial expansions with negative integral powers.