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Fungrim entry: 82373a

∑k=0nFk2=FnFn+1\sum_{k=0}^{n} F_{k}^{2} = F_{n} F_{n + 1}
Assumptions:n∈Z≥0n \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
Sum∑nf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
FibonacciFnF_{n} Fibonacci number
ZZGreaterEqualZ≥n\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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2021-03-15 19:12:00.328586 UTC