Question

estimates of series involving trigonometric functions

score 57 · Answer 1 · 2023-06-02 21:06:26

57

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estimates of series involving trigonometric functions

Published on 02 Jun 2023 - 21:06

score 179 · Answer 2 · 2023-06-09 15:42:27

179

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Question on computing $\sum_{n=1}^\infty \tan^{-1} \left(\frac{3}{n^2 + n - 1}\right)$

Published on 09 Jun 2023 - 15:42

score 57 · Answer 3 · 2023-06-09 21:06:06

57

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Show Fourier series can be rearranged to equal a series

Published on 09 Jun 2023 - 21:06

score 55 · Answer 4 · 2023-06-21 14:53:15

55

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$\int \frac{1}{(\cos x)^{2n+1}}dx$

Published on 21 Jun 2023 - 14:53

score 110 · Answer 5 · 2023-06-25 11:02:35

110

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Show that $\left | \sum_{k=1}^\infty \frac{\left(e^{ik} + \sin(\sqrt 2 k) + \cos(\sqrt 3 k)\right)^3}{k} \right| < 6$

Published on 25 Jun 2023 - 11:02

score 53 · Answer 6 · 2026-03-25 09:50:15

53

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Set of uniqueness of a harmonic series

Published on 25 Mar 2026 - 9:50

score 31 · Answer 7 · 2023-07-03 17:11:48

31

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Find the Fourier trigonometric series of a piece-wise function and then prove a certain sum.

Published on 03 Jul 2023 - 17:11

score 187 · Answer 8 · 2023-07-13 06:09:26

187

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Product of distances from a point on the circle to equidistant points on the circle

Published on 13 Jul 2023 - 6:09

score 382 · Answer 9 · 2026-03-25 23:58:40

382

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Is there an identity for $\sum_{k=0}^{n-1}\csc(w+ k \frac{\pi}{n})\csc(x+ k \frac{\pi}{n})\csc(y+ k \frac{\pi}{n})\csc(z+ k \frac{\pi}{n})$?

Published on 25 Mar 2026 - 23:58

score 39 · Answer 10 · 2023-07-19 14:53:02

39

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Loss of convergence at end point

Published on 19 Jul 2023 - 14:53

score 97 · Answer 11 · 2023-07-24 09:41:27

97

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Prove $\sum_{k=0}^{\infty}a^k\text{cos}kx=\frac{1-a\text{cos}x}{1-2a\text{cos}x+a^2}, \; |a|<1$

Published on 24 Jul 2023 - 9:41

score 93 · Answer 12 · 2023-07-26 05:39:09

93

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Sum of the Sines of the Ratios of Fibonnaci Numbers

Published on 26 Jul 2023 - 5:39

score 85 · Answer 13 · 2023-08-05 20:55:12

85

Views

How can i prove this sum of factorials?

Published on 05 Aug 2023 - 20:55

score 41 · Answer 14 · 2023-08-08 02:59:50

41

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Evaluate the product $\prod\limits_{k=1}^{2^{1999}} (4\sin^2(\frac{k\pi}{2^{2000}})-3)$

Published on 08 Aug 2023 - 2:59

score 647 · Answer 15 · 2023-08-08 11:16:10

647

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Simplifying $3S_1 + 2S_2 + 2S_3$, where $S_1=2\sum_{k=0}^n16^k\tan^4{2^kx}$, $S_2=4\sum_{k=0}^n16^k\tan^2{2^kx}$, $S_3=\sum_{k=0}^n16^k$

Published on 08 Aug 2023 - 11:16

List Question

estimates of series involving trigonometric functions

Question on computing $\sum_{n=1}^\infty \tan^{-1} \left(\frac{3}{n^2 + n - 1}\right)$

Show Fourier series can be rearranged to equal a series

$\int \frac{1}{(\cos x)^{2n+1}}dx$

Show that $\left | \sum_{k=1}^\infty \frac{\left(e^{ik} + \sin(\sqrt 2 k) + \cos(\sqrt 3 k)\right)^3}{k} \right| < 6$

Set of uniqueness of a harmonic series

Find the Fourier trigonometric series of a piece-wise function and then prove a certain sum.

Product of distances from a point on the circle to equidistant points on the circle

Is there an identity for $\sum_{k=0}^{n-1}\csc(w+ k \frac{\pi}{n})\csc(x+ k \frac{\pi}{n})\csc(y+ k \frac{\pi}{n})\csc(z+ k \frac{\pi}{n})$?

Loss of convergence at end point

Prove $\sum_{k=0}^{\infty}a^k\text{cos}kx=\frac{1-a\text{cos}x}{1-2a\text{cos}x+a^2}, \; |a|<1$

Sum of the Sines of the Ratios of Fibonnaci Numbers

How can i prove this sum of factorials?

Evaluate the product $\prod\limits_{k=1}^{2^{1999}} (4\sin^2(\frac{k\pi}{2^{2000}})-3)$

Simplifying $3S_1 + 2S_2 + 2S_3$, where $S_1=2\sum_{k=0}^n16^k\tan^4{2^kx}$, $S_2=4\sum_{k=0}^n16^k\tan^2{2^kx}$, $S_3=\sum_{k=0}^n16^k$

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