Fungrim entry: dea83d

\pi = \lim_{n \to \infty} \frac{4}{{n}^{2}} \sum_{k=0}^{n} \sqrt{{n}^{2} - {k}^{2}}

TeX:

\pi = \lim_{n \to \infty} \frac{4}{{n}^{2}} \sum_{k=0}^{n} \sqrt{{n}^{2} - {k}^{2}}

Definitions:

Fungrim symbol	Notation	Short description
`Pi`	$\pi$	The constant pi (3.14...)
`SequenceLimit`	$\lim_{n \to a} f(n)$	Limiting value of sequence
`Pow`	${a}^{b}$	Power
`Sum`	$\sum_{n} f(n)$	Sum
`Sqrt`	$\sqrt{z}$	Principal square root
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("dea83d"),
    Formula(Equal(Pi, SequenceLimit(Mul(Div(4, Pow(n, 2)), Sum(Sqrt(Sub(Pow(n, 2), Pow(k, 2))), For(k, 0, n))), For(n, Infinity)))))

Topics using this entry

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

2021-03-15 19:12:00.328586 UTC