Question

Showing that $\sum_{n=1}^{\infty}\left(\frac{\sin(22n)}{7n}\right)^3=\frac{1}{2}\left(\pi-\frac{22}{7}\right)^3$

score 756 · Answer 1 · 2026-04-16 05:14:41

756

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Showing that $\sum_{n=1}^{\infty}\left(\frac{\sin(22n)}{7n}\right)^3=\frac{1}{2}\left(\pi-\frac{22}{7}\right)^3$

Published on 16 Apr 2026 - 5:14

score 110 · Answer 2 · 2026-04-09 14:01:21

110

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How to prove, that this chain fraction equals $\frac{4}{\pi}$?

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score 240 · Answer 3 · 2026-04-16 19:51:55

240

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Optimal Fixed-Digit Rational Approximations of $\pi$

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score 271 · Answer 4 · 2026-04-16 09:12:42

271

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score 247 · Answer 5 · 2026-04-13 20:30:03

247

Views

Why does Brent/Salamin algorithm double the digits of $\pi$ with each iteration?

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score 120 · Answer 6 · 2026-04-14 01:32:22

120

Views

Can you precisely calculate $x^{\pi}$ (up to first 200 decimals) without a computer?

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score 157 · Answer 7 · 2026-04-12 08:37:00

157

Views

What does this number sieve have to do with pi?

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score 1.2k · Answer 8 · 2026-04-13 04:00:03

1.2k

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score 608 · Answer 9 · 2026-04-09 22:11:16

608

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score 81 · Answer 10 · 2026-04-16 07:39:55

81

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score 76 · Answer 11 · 2026-04-12 01:51:43

76

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score 219 · Answer 12 · 2026-04-09 19:06:40

219

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score 142 · Answer 13 · 2026-04-15 16:20:45

142

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Summation containing $\pi$ gives an expression containing $e$

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score 667 · Answer 14 · 2026-05-06 14:02:51

667

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score 218 · Answer 15 · 2026-04-10 05:27:31

218

Views

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Published on 10 Apr 2026 - 5:27

List Question

Showing that $\sum_{n=1}^{\infty}\left(\frac{\sin(22n)}{7n}\right)^3=\frac{1}{2}\left(\pi-\frac{22}{7}\right)^3$

How to prove, that this chain fraction equals $\frac{4}{\pi}$?

Optimal Fixed-Digit Rational Approximations of $\pi$

Wallis integral and gamma function

Why does Brent/Salamin algorithm double the digits of $\pi$ with each iteration?

Can you precisely calculate $x^{\pi}$ (up to first 200 decimals) without a computer?

What does this number sieve have to do with pi?

How to show that $\pi^\pi$ is not a integer?

Understanding $\arctan$, with the Leibniz series

Prove that the circumference of a circle is $25\pi$

Are both square roots of -1 valid in Euler's Identity?

Limit approaching pi

Summation containing $\pi$ gives an expression containing $e$

"Distance" between summands in Taylor Series of Cosine

How can Weierstrass product for the gamma function reduce to Wallis formula for $\pi$?

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