Question

Proving $\pi=(27S-36)/(8\sqrt{3})$, where $S=\sum_{n=0}^\infty\frac{\left(\left\lfloor\frac{n}{2}\right\rfloor!\right)^2}{n!}$

score 1k · Answer 1 · 2020-05-24 16:26:09

1k

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Proving $\pi=(27S-36)/(8\sqrt{3})$, where $S=\sum_{n=0}^\infty\frac{\left(\left\lfloor\frac{n}{2}\right\rfloor!\right)^2}{n!}$

Published on 24 May 2020 - 16:26

score 74 · Answer 2 · 2026-03-26 17:53:44

74

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101

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35

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89

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1.6k

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score 636 · Answer 7 · 2026-03-25 18:57:29

636

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Charming approximation of $\pi$: $2\left(\frac{1}{2}\right)^{\phi/2}+2< \pi$, where $\phi$ is the golden ratio

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score 122 · Answer 8 · 2026-03-26 13:00:54

122

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123

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140

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323

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423

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161

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List Question

Proving $\pi=(27S-36)/(8\sqrt{3})$, where $S=\sum_{n=0}^\infty\frac{\left(\left\lfloor\frac{n}{2}\right\rfloor!\right)^2}{n!}$

Way of expressing transcendental number in terms of known mathematical constants?

Unit circle coordinates to pi

Fourierseries where $a_{0}$ isn't what is is supposed to be

Find the function does describe the the percentage of the area that each circle overlaps

Why this approximation for $\pi$ is so accurate?

Charming approximation of $\pi$: $2\left(\frac{1}{2}\right)^{\phi/2}+2< \pi$, where $\phi$ is the golden ratio

Series of square of factorial

Nice inequality ,Prove that $\Gamma\Big(\frac{\sin(x)}{x}\Big)\leq \frac{\pi}{\pi-x}$

Calculate the distance between 2 points on a sinusoidal curve

The intuition of the round value of $e^{i \pi}$

An Interesting Question I Posed to Myself About $\pi$ as an Average.

Trigonometry issue

Express in base π the circumference of a circle of radius 1.

Value of $\pi$ modulo a prime

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