Binomial Theorem

combinatorics

Definition

Binomial Theorem

Given an integer $n\in \mathbb{Z}$ and complex numbers $x,y\in \mathbb{C}$, the binomial theorem states:

$$\sum _{k=0}^n\left(\genfrac{}{}{0ex}{}{n}{k}\right)x^{n-k}{y}^k=(x+y{)}^n$$