Question

Prove or disprove that $ \sum\limits_{k = 1 }^T f(k)=0 $ where $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin(\frac{n(n+1)(2n+1)}{6}x) $

score 655 · Answer 1 · 2018-07-03 09:33:26

655

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Prove or disprove that $ \sum\limits_{k = 1 }^T f(k)=0 $ where $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin(\frac{n(n+1)(2n+1)}{6}x) $

Published on 03 Jul 2018 - 9:33

score 55 · Answer 2 · 2018-07-05 22:37:43

55

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How to convert my equation (Exponential) to cot form?

Published on 05 Jul 2018 - 22:37

score 266 · Answer 3 · 2018-07-06 05:58:48

266

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Polar Curve Fitting

Published on 06 Jul 2018 - 5:58

score 92 · Answer 4 · 2018-07-07 17:44:56

Number of solutions $2^\frac{1}{\sin^2 x_2} \cdot 3^\frac{1}{\sin^2 x_3}\cdot\;\cdots\;\cdot n^\frac{1}{\sin^2 x_n} \leq n!$ with $x_i\in(0,4\pi)$

score 383 · Answer 5 · 2018-07-10 07:03:23

383

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Conjecture about $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin\left(P_r(n) \frac{a \pi}{b}\right) $

Published on 10 Jul 2018 - 7:03

score 311 · Answer 6 · 2018-07-16 09:15:00

311

Views

Extended conjecture for $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin\left(\sum\limits_{k = 1 }^\infty \frac{a_k \pi}{b_k}P_k(n) \right)$

Published on 16 Jul 2018 - 9:15

score 87 · Answer 7 · 2018-07-18 14:23:52

87

Views

Expansion of $x$ in powers of $u$

Published on 18 Jul 2018 - 14:23

score 29 · Answer 8 · 2018-07-24 16:48:52

29

Views

$\sum_{k=1}^n\sin kx=\frac{\cos\left(\frac{1}2x\right)-\cos\left(n+\frac{1}2\right)x}{2\sin(x/2)},x\neq0,\pm\pi,\pm 2\pi,\ldots$

Published on 24 Jul 2018 - 16:48

score 174 · Answer 9 · 2026-03-25 11:54:13

174

Views

Any suggestions on how to compute $\limsup |\cos n|^{n^2}$?

Published on 25 Mar 2026 - 11:54

score 43 · Answer 10 · 2018-08-07 19:06:15

43

Views

Summation of Finite trigonometrical series

Published on 07 Aug 2018 - 19:06

score 44 · Answer 11 · 2018-08-10 20:40:45

44

Views

Closed form for a conditional trigonometric series

Published on 10 Aug 2018 - 20:40

score 76 · Answer 12 · 2018-08-19 04:54:27

Identical equation $\sin(\frac{nx}{2^{n-1}})=\sin x\times \sin(x+\pi/n)\times \cdot\cdot\cdot \times \sin(x+\frac{(n-1)\pi}{n}) $

score 382 · Answer 13 · 2018-08-22 20:32:02

382

Views

Sum of binomial coefficients in Gould tables

Published on 22 Aug 2018 - 20:32

score 404 · Answer 14 · 2018-08-25 15:36:53

404

Views

Simplify $\sum_{k = 1}^n \tan(k) \tan(k - 1)$ by first proving $\tan(k)\tan(k - 1) = \frac{\tan(k) - \tan(k - 1)}{\tan(1)} - 1$

Published on 25 Aug 2018 - 15:36

score 131 · Answer 15 · 2018-08-25 20:54:24

131

Views

Probably this :$\sum_{n=2}^{\infty}(-1)^n\frac{\arctan{(1-2^n)}\log n \tan{(1-2^{-n})}}{n^3\sqrt{n}\log \log n }$ is Euler constant

Published on 25 Aug 2018 - 20:54

List Question

Prove or disprove that $ \sum\limits_{k = 1 }^T f(k)=0 $ where $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin(\frac{n(n+1)(2n+1)}{6}x) $

How to convert my equation (Exponential) to cot form?

Polar Curve Fitting

Number of solutions $2^\frac{1}{\sin^2 x_2} \cdot 3^\frac{1}{\sin^2 x_3}\cdot\;\cdots\;\cdot n^\frac{1}{\sin^2 x_n} \leq n!$ with $x_i\in(0,4\pi)$

Conjecture about $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin\left(P_r(n) \frac{a \pi}{b}\right) $

Extended conjecture for $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin\left(\sum\limits_{k = 1 }^\infty \frac{a_k \pi}{b_k}P_k(n) \right)$

Expansion of $x$ in powers of $u$

$\sum_{k=1}^n\sin kx=\frac{\cos\left(\frac{1}2x\right)-\cos\left(n+\frac{1}2\right)x}{2\sin(x/2)},x\neq0,\pm\pi,\pm 2\pi,\ldots$

Any suggestions on how to compute $\limsup |\cos n|^{n^2}$?

Summation of Finite trigonometrical series

Closed form for a conditional trigonometric series

Identical equation $\sin(\frac{nx}{2^{n-1}})=\sin x\times \sin(x+\pi/n)\times \cdot\cdot\cdot \times \sin(x+\frac{(n-1)\pi}{n}) $

Sum of binomial coefficients in Gould tables

Simplify $\sum_{k = 1}^n \tan(k) \tan(k - 1)$ by first proving $\tan(k)\tan(k - 1) = \frac{\tan(k) - \tan(k - 1)}{\tan(1)} - 1$

Probably this :$\sum_{n=2}^{\infty}(-1)^n\frac{\arctan{(1-2^n)}\log n \tan{(1-2^{-n})}}{n^3\sqrt{n}\log \log n }$ is Euler constant

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