ThmDex – An index of mathematical definitions, results, and conjectures.
Basic real golden ratio is limit of successive terms in the Fibonacci natural number sequence
Formulation 0
Let $\varphi : = (1 + \sqrt{5}) / 2$ be the D2137: Basic real golden ratio.
Let $F_0, F_1, F_2, \ldots \in \mathbb{N}$ be the D4594: Fibonacci natural number sequence.
Then \begin{equation} \lim_{n \to \infty} \frac{F_{n + 1}}{F_n} = \varphi \end{equation}