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Fungrim entry: f95561

k=0n(1)k+1(nk)Fk=Fn\sum_{k=0}^{n} {\left(-1\right)}^{k + 1} {n \choose k} F_{k} = F_{n}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\sum_{k=0}^{n} {\left(-1\right)}^{k + 1} {n \choose k} F_{k} = F_{n}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Binomial(nk){n \choose k} Binomial coefficient
FibonacciFnF_{n} Fibonacci number
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("f95561"),
    Formula(Equal(Sum(Mul(Mul(Pow(-1, Add(k, 1)), Binomial(n, k)), Fibonacci(k)), For(k, 0, n)), Fibonacci(n))),
    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