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ThmDex – An index of mathematical definitions, results, and conjectures.
Definitions
,
Results
,
Conjectures
Result R3611 on
D2167: Binomial coefficient
Subresult of
R2788: Real binomial theorem
Formulation 0
Let
x
∈
R
be a
D993: Real number
.
Let
n
∈
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