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Fungrim entry: 6d8bf0

n=01F2n=752\sum_{n=0}^{\infty} \frac{1}{F_{{2}^{n}}} = \frac{7 - \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}}} = \frac{7 - \sqrt{5}}{2}
Definitions:
Fungrim symbol Notation Short description
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
Infinity\infty Positive infinity
Sqrtz\sqrt{z} Principal square root
Source code for this entry:
Entry(ID("6d8bf0"),
    Formula(Equal(Sum(Div(1, Fibonacci(Pow(2, n))), For(n, 0, Infinity)), Div(Sub(7, Sqrt(5)), 2))),
    References("J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987."))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-22 15:43:45.410764 UTC