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Fungrim entry: 3bb7e4

k=0nF2k=F2n+11\sum_{k=0}^{n} F_{2 k} = F_{2 n + 1} - 1
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\sum_{k=0}^{n} F_{2 k} = F_{2 n + 1} - 1

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
FibonacciFnF_{n} Fibonacci number
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("3bb7e4"),
    Formula(Equal(Sum(Fibonacci(Mul(2, k)), Tuple(k, 0, n)), Sub(Fibonacci(Add(Mul(2, n), 1)), 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.

2019-08-21 11:44:15.926409 UTC