AlgèbreBinomial theoremBinomial theoremDefinitionPropositionLet (a,b)∈C2(a,b) \in \mathbb C^2(a,b)∈C2 and n∈Nn \in \mathbb Nn∈N, we have:(a+b)n=∑p=0n(np)apbn−p.(a+b)^n = \sum_{p=0}^n \binom{n}{p}a^pb^{n-p}.(a+b)n=p=0∑n(pn)apbn−p.ProofWe proceed by recurrence, using Pascal's formula.