Question

Summation of $\arccos\left(\frac{n^2+r^2+r}{\sqrt{(n^2+r^2+r)^2+n^2}}\right)$

score 135 · Answer 1 · 2018-12-17 17:19:39

135

Views

Summation of $\arccos\left(\frac{n^2+r^2+r}{\sqrt{(n^2+r^2+r)^2+n^2}}\right)$

Published on 17 Dec 2018 - 17:19

score 43 · Answer 2 · 2026-03-25 15:17:51

43

Views

Fallacious moving of powers resulting with a correct trigonometric series identity.

Published on 25 Mar 2026 - 15:17

score 381 · Answer 3 · 2018-12-27 04:44:37

381

Views

Compute $\sum\limits_{j = 0}^{m - 1} \left(c_j + 1\right)\ln\left(c_j + 1\right)$ where $c_j = \cos\left(\frac{\pi}{2m}\left(1 + 2j\right) \right)$

Published on 27 Dec 2018 - 4:44

score 99 · Answer 4 · 2018-12-30 02:43:08

99

Views

Series expansion (likely Maclaurin) of integral

Published on 30 Dec 2018 - 2:43

score 1.2k · Answer 5 · 2019-01-04 11:23:52

1.2k

Views

If $\sin(\pi x)=a_0+\sum\limits_{n=1}^{\infty}a_n \cos(n\pi x)$ for $0<x<1$ then what is the value of $(a_0+a_1)\pi$?

Published on 04 Jan 2019 - 11:23

score 153 · Answer 6 · 2026-03-25 04:40:28

153

Views

Non zero solution of $3x\cos(x) + (-3 + x^2)\sin(x)=0$

Published on 25 Mar 2026 - 4:40

score 825 · Answer 7 · 2019-01-07 23:03:10

825

Views

Prove $\sum_{k=1}^m \cot^2 k\pi/(2m+1)=m(2m-1)/3$

Published on 07 Jan 2019 - 23:03

score 44 · Answer 8 · 2026-03-25 14:25:14

44

Views

Would sine trigonometric series $f(x)$ for approximating $g(x) = x$ always be $f(x) \leq x$ for $0 \leq x \leq \pi$?

Published on 25 Mar 2026 - 14:25

score 77 · Answer 9 · 2026-03-25 14:25:10

77

Views

Is $f(x) \leq x$ for $0 \leq x \leq \pi$ when sine series $f(x)$ are used to approximate $x$ based on derivatives at $x=0$?

Published on 25 Mar 2026 - 14:25

score 37 · Answer 10 · 2019-01-20 18:11:56

37

Views

What type of waveform is described by this fourier series

Published on 20 Jan 2019 - 18:11

score 65 · Answer 11 · 2019-01-21 21:20:17

65

Views

Infinite Sum of a Converging Series of Inverse Cosines

Published on 21 Jan 2019 - 21:20

score 1.2k · Answer 12 · 2019-01-26 02:09:56

1.2k

Views

$\sum_{n=1}^\infty a_n \cos nx$ unbounded near $0$ if $\sum a_n$ diverges?

Published on 26 Jan 2019 - 2:09

score 111 · Answer 13 · 2019-02-12 16:46:03

111

Views

Finding all real $x$ such that $1+\sum_{j=1}^n\sin{\frac{j\pi x}{n+1}} = 0$, where $n=18$.

Published on 12 Feb 2019 - 16:46

score 543 · Answer 14 · 2019-02-14 17:39:11

543

Views

Is $\sum\limits_{n=1}^\infty \arctan \frac x {n^2}$ continuous?

Published on 14 Feb 2019 - 17:39

score 100 · Answer 15 · 2019-02-19 19:30:55

100

Views

Prove the following infinite trig product by induction.

Published on 19 Feb 2019 - 19:30

List Question

Summation of $\arccos\left(\frac{n^2+r^2+r}{\sqrt{(n^2+r^2+r)^2+n^2}}\right)$

Fallacious moving of powers resulting with a correct trigonometric series identity.

Compute $\sum\limits_{j = 0}^{m - 1} \left(c_j + 1\right)\ln\left(c_j + 1\right)$ where $c_j = \cos\left(\frac{\pi}{2m}\left(1 + 2j\right) \right)$

Series expansion (likely Maclaurin) of integral

If $\sin(\pi x)=a_0+\sum\limits_{n=1}^{\infty}a_n \cos(n\pi x)$ for $0<x<1$ then what is the value of $(a_0+a_1)\pi$?

Non zero solution of $3x\cos(x) + (-3 + x^2)\sin(x)=0$

Prove $\sum_{k=1}^m \cot^2 k\pi/(2m+1)=m(2m-1)/3$

Would sine trigonometric series $f(x)$ for approximating $g(x) = x$ always be $f(x) \leq x$ for $0 \leq x \leq \pi$?

Is $f(x) \leq x$ for $0 \leq x \leq \pi$ when sine series $f(x)$ are used to approximate $x$ based on derivatives at $x=0$?

What type of waveform is described by this fourier series

Infinite Sum of a Converging Series of Inverse Cosines

$\sum_{n=1}^\infty a_n \cos nx$ unbounded near $0$ if $\sum a_n$ diverges?

Finding all real $x$ such that $1+\sum_{j=1}^n\sin{\frac{j\pi x}{n+1}} = 0$, where $n=18$.

Is $\sum\limits_{n=1}^\infty \arctan \frac x {n^2}$ continuous?

Prove the following infinite trig product by induction.

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