ThmDex – An index of mathematical definitions, results, and conjectures.

Processing math: 25%

Result R4673 on D1932: Standard natural real exponential function
Subresult of R3385: Standard approximating sequence for the natural exponential function

Napier's constant equals a limit of products with factors nearing one

Formulation 0

Let

Then

$\begin{equation} \lim_{n \to \infty} \left( 1 + \frac{1}{n} \right)^n = e \end{equation}$

Proofs

Proof 1

Let

$\square$