Fungrim home page

Fungrim entry: 31eecc

π=2n=0atan ⁣(1F2n+1)\pi = 2 \sum_{n=0}^{\infty} \operatorname{atan}\!\left(\frac{1}{F_{2 n + 1}}\right)
TeX:
\pi = 2 \sum_{n=0}^{\infty} \operatorname{atan}\!\left(\frac{1}{F_{2 n + 1}}\right)
Definitions:
Fungrim symbol Notation Short description
Piπ\pi The constant pi (3.14...)
Sumnf(n)\sum_{n} f(n) Sum
Atanatan(z)\operatorname{atan}(z) Inverse tangent
FibonacciFnF_{n} Fibonacci number
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("31eecc"),
    Formula(Equal(Pi, Mul(2, Sum(Atan(Div(1, Fibonacci(Add(Mul(2, n), 1)))), For(n, 0, Infinity))))))

Topics using this entry

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

2020-08-27 09:56:25.682319 UTC