Fungrim home page

Fungrim entry: e1e106

\pi = \lim_{k \to \infty} \frac{{16}^{k}}{k {{2 k \choose k}}^{2}}

TeX:

\pi = \lim_{k \to \infty} \frac{{16}^{k}}{k {{2 k \choose k}}^{2}}

Definitions:

Fungrim symbol	Notation	Short description
`ConstPi`	$\pi$	The constant pi (3.14...)
`SequenceLimit`	$\lim_{n \to a} f\!\left(n\right)$	Limiting value of sequence
`Pow`	${a}^{b}$	Power
`Binomial`	${n \choose k}$	Binomial coefficient
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("e1e106"),
    Formula(Equal(ConstPi, SequenceLimit(Div(Pow(16, k), Mul(k, Pow(Binomial(Mul(2, k), k), 2))), k, Infinity))))

Topics using this entry

Pi

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

2019-06-18 07:49:59.356594 UTC