Fungrim home page

Fungrim entry: 3bb7e4

∑k=0nF2k=F2n+1−1\sum_{k=0}^{n} F_{2 k} = F_{2 n + 1} - 1
Assumptions:n∈Z≥0n \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
Sum∑nf(n)\sum_{n} f(n) Sum
FibonacciFnF_{n} Fibonacci number
ZZGreaterEqualZ≥n\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)), For(k, 0, n)), Sub(Fibonacci(Add(Mul(2, n), 1)), 1))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

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