Question

Find sum of $\frac{1}{\sin\theta\cdot \sin2\theta} + \frac{1}{\sin2\theta\cdot \sin3\theta} + \cdots + \frac{1}{\sin n \theta \sin (n+1)\theta}$

score 139 · Answer 1 · 2014-05-29 07:40:28

Find sum of $\frac{1}{\sin\theta\cdot \sin2\theta} + \frac{1}{\sin2\theta\cdot \sin3\theta} + \cdots + \frac{1}{\sin n \theta \sin (n+1)\theta}$

score 624 · Answer 2 · 2014-06-03 02:05:10

624

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A sine integral

Published on 03 Jun 2014 - 2:05

score 367 · Answer 3 · 2014-06-10 14:51:19

367

Views

Find the limit of $\prod_{k = 4}^{\infty}\cos\left(\pi \over k\right)$

Published on 10 Jun 2014 - 14:51

score 68 · Answer 4 · 2014-06-10 15:58:45

68

Views

Closed-form expressions for coefficients $a_k$ in $2^{2n-1}\sinh^{2n}(x)=\sum_{k=0}^n a_k \cosh(2kx)$

Published on 10 Jun 2014 - 15:58

score 147 · Answer 5 · 2014-06-11 10:31:30

147

Views

$\int _0^{\pi }\:\sum _{n=0}^{\infty \:}\frac{n\cdot \sin \left(nx\right)}{e^n}dx=\frac{2e}{e^2-1}$

Published on 11 Jun 2014 - 10:31

score 130 · Answer 6 · 2014-06-14 04:14:58

130

Views

Is there a relationship between a function's period and number of roots?

Published on 14 Jun 2014 - 4:14

score 1k · Answer 7 · 2014-06-17 23:17:09

1k

Views

Proving that $\sum^n_{k=1} e^{ik\theta}=\sum^n_{i=1}\cos k\theta +i\sum^n_{k=1}\sin k\theta$.

Published on 17 Jun 2014 - 23:17

score 114 · Answer 8 · 2014-07-03 12:54:39

114

Views

Evaluation of a trigonometric series

Published on 03 Jul 2014 - 12:54

score 108 · Answer 9 · 2014-07-25 02:20:29

108

Views

Solve $\sin^2 x − \cos^2 x = \sin x$, when $x\in -\pi ≤ x ≤\pi$

Published on 25 Jul 2014 - 2:20

score 1.9k · Answer 10 · 2014-07-28 21:41:48

1.9k

Views

Differentiability of the sum of the series $\sum_k \sin(kx)/k^2$

Published on 28 Jul 2014 - 21:41

score 633 · Answer 11 · 2014-07-30 16:28:13

633

Views

Hard Trigonometric Equation

Published on 30 Jul 2014 - 16:28

score 461 · Answer 12 · 2014-08-02 21:51:55

461

Views

Sequence of trigonometric polynomials which converges to an integrable function

Published on 02 Aug 2014 - 21:51

score 728 · Answer 13 · 2026-03-25 10:15:40

728

Views

Problem involving summing exponential series:

Published on 25 Mar 2026 - 10:15

score 535 · Answer 14 · 2014-08-06 00:59:26

535

Views

Trigonometric series problem: finding a second valid solution.

Published on 06 Aug 2014 - 0:59

score 226 · Answer 15 · 2026-03-26 03:18:48

226

Views

Sum of Complex series

Published on 26 Mar 2026 - 3:18

List Question

Find sum of $\frac{1}{\sin\theta\cdot \sin2\theta} + \frac{1}{\sin2\theta\cdot \sin3\theta} + \cdots + \frac{1}{\sin n \theta \sin (n+1)\theta}$

A sine integral

Find the limit of $\prod_{k = 4}^{\infty}\cos\left(\pi \over k\right)$

Closed-form expressions for coefficients $a_k$ in $2^{2n-1}\sinh^{2n}(x)=\sum_{k=0}^n a_k \cosh(2kx)$

$\int _0^{\pi }\:\sum _{n=0}^{\infty \:}\frac{n\cdot \sin \left(nx\right)}{e^n}dx=\frac{2e}{e^2-1}$

Is there a relationship between a function's period and number of roots?

Proving that $\sum^n_{k=1} e^{ik\theta}=\sum^n_{i=1}\cos k\theta +i\sum^n_{k=1}\sin k\theta$.

Evaluation of a trigonometric series

Solve $\sin^2 x − \cos^2 x = \sin x$, when $x\in -\pi ≤ x ≤\pi$

Differentiability of the sum of the series $\sum_k \sin(kx)/k^2$

Hard Trigonometric Equation

Sequence of trigonometric polynomials which converges to an integrable function

Problem involving summing exponential series:

Trigonometric series problem: finding a second valid solution.

Sum of Complex series

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