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Fungrim entry: 9c53d7

Fn>φn15F_{n} > \frac{{\varphi}^{n} - 1}{\sqrt{5}}
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
TeX:
F_{n} > \frac{{\varphi}^{n} - 1}{\sqrt{5}}

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
GoldenRatioφ\varphi The golden ratio (1.618...)
Sqrtz\sqrt{z} Principal square root
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("9c53d7"),
    Formula(Greater(Fibonacci(n), Div(Sub(Pow(GoldenRatio, n), 1), Sqrt(5)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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

2019-08-17 11:32:46.829430 UTC