Question

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

score 138 · Answer 1 · 2026-04-15 14:05:36

138

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

Published on 15 Apr 2026 - 14:05

score 45 · Answer 2 · 2026-04-16 04:24:28

45

Views

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

Published on 16 Apr 2026 - 4:24

score 384 · Answer 3 · 2026-04-16 05:49:11

384

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 16 Apr 2026 - 5:49

score 102 · Answer 4 · 2026-04-11 09:30:54

102

Views

Series expansion (likely Maclaurin) of integral

Published on 11 Apr 2026 - 9:30

score 1.2k · Answer 5 · 2026-04-15 13:29:09

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 15 Apr 2026 - 13:29

score 155 · Answer 6 · 2026-04-16 21:52:39

155

Views

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

Published on 16 Apr 2026 - 21:52

score 828 · Answer 7 · 2026-04-14 21:47:09

828

Views

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

Published on 14 Apr 2026 - 21:47

score 46 · Answer 8 · 2026-04-16 04:05:49

46

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 16 Apr 2026 - 4:05

score 79 · Answer 9 · 2026-04-16 00:42:26

79

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 16 Apr 2026 - 0:42

score 40 · Answer 10 · 2026-04-14 18:37:09

40

Views

What type of waveform is described by this fourier series

Published on 14 Apr 2026 - 18:37

score 68 · Answer 11 · 2026-04-13 02:18:00

68

Views

Infinite Sum of a Converging Series of Inverse Cosines

Published on 13 Apr 2026 - 2:18

score 1.2k · Answer 12 · 2026-04-16 10:42:31

1.2k

Views

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

Published on 16 Apr 2026 - 10:42

score 114 · Answer 13 · 2026-04-17 02:59:02

114

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 17 Apr 2026 - 2:59

score 546 · Answer 14 · 2026-04-11 05:22:53

546

Views

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

Published on 11 Apr 2026 - 5:22

score 103 · Answer 15 · 2026-04-15 16:37:23

103

Views

Prove the following infinite trig product by induction.

Published on 15 Apr 2026 - 16:37

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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