ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation 0
Let $x \in \mathbb{R}$ be a D993: Real number.
Let $n \in \mathbb{N}$ be a D996: Natural number.
Then \begin{equation} (1 + x)^n = \sum_{m = 0}^n \binom{n}{m} x^m \end{equation}
Proofs
Proof 0
Let $x \in \mathbb{R}$ be a D993: Real number.
Let $n \in \mathbb{N}$ be a D996: Natural number.
This result is a particular case of R2788: Real binomial theorem. $\square$