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Fungrim entry: 82373a

k=0nFk2=FnFn+1\sum_{k=0}^{n} F_{k}^{2} = F_{n} F_{n + 1}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\sum_{k=0}^{n} F_{k}^{2} = F_{n} F_{n + 1}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
FibonacciFnF_{n} Fibonacci number
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("82373a"),
    Formula(Equal(Sum(Pow(Fibonacci(k), 2), For(k, 0, n)), Mul(Fibonacci(n), Fibonacci(Add(n, 1))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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

2019-10-05 13:11:19.856591 UTC