Fungrim entry: d56025

\lim_{n \to \infty} \frac{F_{n + m}}{F_{n}} = {\varphi}^{m}

Assumptions:

m \in \mathbb{Z}

TeX:

\lim_{n \to \infty} \frac{F_{n + m}}{F_{n}} = {\varphi}^{m}

m \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`SequenceLimit`	$\lim_{n \to a} f(n)$	Limiting value of sequence
`Fibonacci`	$F_{n}$	Fibonacci number
`Infinity`	$\infty$	Positive infinity
`Pow`	${a}^{b}$	Power
`GoldenRatio`	$\varphi$	The golden ratio (1.618...)
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("d56025"),
    Formula(Equal(SequenceLimit(Div(Fibonacci(Add(n, m)), Fibonacci(n)), For(n, Infinity)), Pow(GoldenRatio, m))),
    Variables(m),
    Assumptions(Element(m, ZZ)))

Topics using this entry

Fibonacci numbers

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC