Question

Proving that $\left(\frac{\pi}{3} \right)^{2}=1+2\sum_{k=1}^{\infty}\frac{(2k+1)\zeta(2k+2)}{3^{2k+2}}$.

score 176 · Answer 1 · 2014-02-19 16:19:25

176

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Proving that $\left(\frac{\pi}{3} \right)^{2}=1+2\sum_{k=1}^{\infty}\frac{(2k+1)\zeta(2k+2)}{3^{2k+2}}$.

Published on 19 Feb 2014 - 16:19

score 729 · Answer 2 · 2026-03-28 11:22:05

729

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Visual explanation of $\pi$ series definition

Published on 28 Mar 2026 - 11:22

score 17.5k · Answer 3 · 2014-02-20 04:17:43

17.5k

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Why is the integral of sec^2(x) from 0 to pi infinity?

Published on 20 Feb 2014 - 4:17

score 91 · Answer 4 · 2014-02-23 01:41:05

91

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Ratios of right triangle integer multiples to PI

Published on 23 Feb 2014 - 1:41

score 273 · Answer 5 · 2014-02-24 07:15:00

273

Views

What would be an elementary way to prove that $3<\pi<4$

Published on 24 Feb 2014 - 7:15

score 4.1k · Answer 6 · 2014-02-24 07:46:43

4.1k

Views

how do i prove that $\sin(\pi/4)=\cos(\pi/4)$?

Published on 24 Feb 2014 - 7:46

score 10.8k · Answer 7 · 2014-02-25 02:26:01

10.8k

Views

Interesting and unexpected applications of $\pi$

Published on 25 Feb 2014 - 2:26

score 655 · Answer 8 · 2014-02-26 19:07:54

655

Views

Is it possible to calculate inverse sine without using pi?

Published on 26 Feb 2014 - 19:07

score 213 · Answer 9 · 2014-02-28 09:05:00

213

Views

What are the principle behind calculation of pi

Published on 28 Feb 2014 - 9:05

score 2.9k · Answer 10 · 2014-03-04 23:54:03

2.9k

Views

Find the F(x) based on given points

Published on 04 Mar 2014 - 23:54

score 11.5k · Answer 11 · 2014-03-06 15:27:22

11.5k

Views

Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$

Published on 06 Mar 2014 - 15:27

score 310 · Answer 12 · 2014-03-06 21:52:36

310

Views

Not $\pi$ - What if I used $3$? Teaching $\pi$ discovery to K-6th grade

Published on 06 Mar 2014 - 21:52

score 93 · Answer 13 · 2014-03-07 10:40:10

93

Views

Prove that : $\lvert s_n - \frac \pi 4\rvert \le \frac 1 {2n+1}$, where $s_n = \sum^{n-1}_{j=0} \frac {(-1)^j} {2j+1}$

Published on 07 Mar 2014 - 10:40

score 210 · Answer 14 · 2014-03-10 11:58:18

210

Views

Is my intuition wrong?

Published on 10 Mar 2014 - 11:58

score 160 · Answer 15 · 2017-04-11 02:15:18

160

Views

How to count beyond $2\pi$?

Published on 11 Apr 2017 - 2:15

List Question

Proving that $\left(\frac{\pi}{3} \right)^{2}=1+2\sum_{k=1}^{\infty}\frac{(2k+1)\zeta(2k+2)}{3^{2k+2}}$.

Visual explanation of $\pi$ series definition

Why is the integral of sec^2(x) from 0 to pi infinity?

Ratios of right triangle integer multiples to PI

What would be an elementary way to prove that $3<\pi<4$

how do i prove that $\sin(\pi/4)=\cos(\pi/4)$?

Interesting and unexpected applications of $\pi$

Is it possible to calculate inverse sine without using pi?

What are the principle behind calculation of pi

Find the F(x) based on given points

Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$

Not $\pi$ - What if I used $3$? Teaching $\pi$ discovery to K-6th grade

Prove that : $\lvert s_n - \frac \pi 4\rvert \le \frac 1 {2n+1}$, where $s_n = \sum^{n-1}_{j=0} \frac {(-1)^j} {2j+1}$

Is my intuition wrong?

How to count beyond $2\pi$?

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