Question

Evaluate the sum of the infinite series $1+\cos x + \cos^2 x + \cos ^3 x ...$ for $0<x<\pi$

score 697 · Answer 1 · 2026-04-16 18:55:04

697

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Evaluate the sum of the infinite series $1+\cos x + \cos^2 x + \cos ^3 x ...$ for $0<x<\pi$

Published on 16 Apr 2026 - 18:55

score 135 · Answer 2 · 2026-04-11 00:12:35

135

Views

eliminating parameters

Published on 11 Apr 2026 - 0:12

score 226 · Answer 3 · 2026-04-14 01:14:00

226

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Evaluation of the sum $\sum\limits_{n=1}^{\infty}\frac1n\sin\frac1n$

Published on 14 Apr 2026 - 1:14

score 57 · Answer 4 · 2026-04-16 15:53:16

57

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$\sum_{k=0}^{n-1}\frac{1}{1-2x\cos\frac{2k\pi}{n}+x^2}$

Published on 16 Apr 2026 - 15:53

score 438 · Answer 5 · 2026-04-09 02:52:36

438

Views

Is there better series to calculate sinh and cosh

Published on 09 Apr 2026 - 2:52

score 834 · Answer 6 · 2026-04-11 13:46:24

834

Views

Complex sum of sine and cosine functions

Published on 11 Apr 2026 - 13:46

score 247 · Answer 7 · 2026-04-16 21:54:17

247

Views

Closed form of :$ \int_{-\infty}^{\infty}\arctan\left(e^{-x^2 \text{erf}(x)}\right)\,\arctan\left(e^{x^2\text{erf(x)}}\right)\,dx $

Published on 16 Apr 2026 - 21:54

score 58 · Answer 8 · 2026-04-12 03:26:31

58

Views

Calculating Arc Hyperbolic CoTangent faster than using a standard power series

Published on 12 Apr 2026 - 3:26

score 890 · Answer 9 · 2026-04-15 18:10:36

890

Views

Prove that trigonometric series is/isn't a Fourier series

Published on 15 Apr 2026 - 18:10

score 75 · Answer 10 · 2026-04-12 09:12:39

75

Views

Calculating Arc Hyperbolic CoSecant faster than using a standard power series

Published on 12 Apr 2026 - 9:12

score 210 · Answer 11 · 2026-04-15 14:05:27

210

Views

Sum this series: $1+\cos{\theta}\sec{\theta}+\cos{2\theta}\sec^2{\theta}+\cdots+\cos{n\theta}\sec^n{\theta}$

Published on 15 Apr 2026 - 14:05

score 44 · Answer 12 · 2026-03-25 22:03:10

44

Views

Sums of trigonometric functions and polynomials

Published on 25 Mar 2026 - 22:03

score 54 · Answer 13 · 2026-04-15 13:19:55

54

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If $(1-\cos{x})^{n+1}=\sum_{k=0}^\infty c_k\cos{kt}$ for some integers $c_k$, then what is $\sum_{k=0}^\infty kc_k$?

Published on 15 Apr 2026 - 13:19

score 98 · Answer 14 · 2026-04-10 06:29:49

98

Views

Complex sum of sine and cosine function

Published on 10 Apr 2026 - 6:29

score 105 · Answer 15 · 2026-04-16 11:21:47

105

Views

Deducing that $cos( \frac{2π}{5}) = \frac{-1+ \sqrt{5}}{4}$

Published on 16 Apr 2026 - 11:21

List Question

Evaluate the sum of the infinite series $1+\cos x + \cos^2 x + \cos ^3 x ...$ for $0<x<\pi$

eliminating parameters

Evaluation of the sum $\sum\limits_{n=1}^{\infty}\frac1n\sin\frac1n$

$\sum_{k=0}^{n-1}\frac{1}{1-2x\cos\frac{2k\pi}{n}+x^2}$

Is there better series to calculate sinh and cosh

Complex sum of sine and cosine functions

Closed form of :$ \int_{-\infty}^{\infty}\arctan\left(e^{-x^2 \text{erf}(x)}\right)\,\arctan\left(e^{x^2\text{erf(x)}}\right)\,dx $

Calculating Arc Hyperbolic CoTangent faster than using a standard power series

Prove that trigonometric series is/isn't a Fourier series

Calculating Arc Hyperbolic CoSecant faster than using a standard power series

Sum this series: $1+\cos{\theta}\sec{\theta}+\cos{2\theta}\sec^2{\theta}+\cdots+\cos{n\theta}\sec^n{\theta}$

Sums of trigonometric functions and polynomials

If $(1-\cos{x})^{n+1}=\sum_{k=0}^\infty c_k\cos{kt}$ for some integers $c_k$, then what is $\sum_{k=0}^\infty kc_k$?

Complex sum of sine and cosine function

Deducing that $cos( \frac{2π}{5}) = \frac{-1+ \sqrt{5}}{4}$

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