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 753 · Answer 1 · 2019-05-27 20:50:11

753

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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 27 May 2019 - 20:50

score 109 · Answer 2 · 2026-03-25 12:54:24

109

Views

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236

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268

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score 244 · Answer 5 · 2019-06-07 20:21:25

244

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score 117 · Answer 6 · 2019-06-07 23:28:47

117

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score 154 · Answer 7 · 2019-06-12 20:55:16

154

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1.2k

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605

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score 79 · Answer 10 · 2026-03-25 17:40:49

79

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score 73 · Answer 11 · 2019-06-26 18:39:25

73

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216

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score 139 · Answer 13 · 2019-07-04 03:54:26

139

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score 660 · Answer 14 · 2026-03-20 00:19:16

660

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score 215 · Answer 15 · 2019-07-07 11:10:41

215

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Published on 07 Jul 2019 - 11:10

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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