ThmDex – An index of mathematical definitions, results, and conjectures.
Standard approximating sequence for the natural exponential function
Formulation 0
Let $e$ be the D169: Napier's constant.
Let $x \in \mathbb{R}$ be a D993: Real number.
Then \begin{equation} \lim_{n \to \infty} \left( 1 + \frac{x}{n} \right)^n = e^x \end{equation}
Subresults
R4673: Napier's constant equals a limit of products with factors nearing one
Proofs
Proof 0
Let $e$ be the D169: Napier's constant.
Let $x \in \mathbb{R}$ be a D993: Real number.
This result is a particular case of R3304: Approximating sequence for the natural exponential function. $\square$