Aller au contenu principal

Binomial theorem

Definition

Proposition

Let (a,b)C2(a,b) \in \mathbb C^2 and nNn \in \mathbb N, we have:

(a+b)n=p=0n(np)apbnp.(a+b)^n = \sum_{p=0}^n \binom{n}{p}a^pb^{n-p}.
Proof

We proceed by recurrence, using Pascal's formula.