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Fungrim entry: ae9d30

∑n=0∞1F2n+1+1=52\sum_{n=0}^{\infty} \frac{1}{F_{2 n + 1} + 1} = \frac{\sqrt{5}}{2}
References:
  • J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987.
TeX:
\sum_{n=0}^{\infty} \frac{1}{F_{2 n + 1} + 1} = \frac{\sqrt{5}}{2}
Definitions:
Fungrim symbol Notation Short description
Sum∑nf(n)\sum_{n} f(n) Sum
FibonacciFnF_{n} Fibonacci number
Infinity∞\infty Positive infinity
Sqrtz\sqrt{z} Principal square root
Source code for this entry:
Entry(ID("ae9d30"),
    Formula(Equal(Sum(Div(1, Add(Fibonacci(Add(Mul(2, n), 1)), 1)), For(n, 0, Infinity)), Div(Sqrt(5), 2))),
    References("J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987."))

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2021-03-15 19:12:00.328586 UTC