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}

Proofs

Proof 0

Let $e$ be the D169: Napier's constant.
Let $x \in \mathbb{R}$ be a D993: Real number.