Question

Simplify $\sin(\alpha)+\sin(\alpha+x)+\sin(\alpha+2x)+\sin(\alpha+3x)+ \dotsb +\sin(\alpha+nx)$

score 65 · Answer 1 · 2026-04-17 12:30:33

65

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Simplify $\sin(\alpha)+\sin(\alpha+x)+\sin(\alpha+2x)+\sin(\alpha+3x)+ \dotsb +\sin(\alpha+nx)$

Published on 17 Apr 2026 - 12:30

score 53 · Answer 2 · 2026-04-14 21:54:08

53

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Convergent series with trigonometric functions like $a_{0}=m, a_{2n-1}=\sin(a_{2n-2}), a_{2n}=\cos(a_{2n-1})$

Published on 14 Apr 2026 - 21:54

score 74 · Answer 3 · 2026-04-17 01:24:37

74

Views

Proving a general formula for $\sum_{m=0}^{n}(-1)^m\binom{n}{m} \sin(a+(n-m)h)$

Published on 17 Apr 2026 - 1:24

score 117 · Answer 4 · 2026-04-14 06:47:18

117

Views

For rotation matrix $A$, find $B = A^4- A^3 + A^2 - A$

Published on 14 Apr 2026 - 6:47

score 125 · Answer 5 · 2026-04-13 18:36:23

125

Views

Why are these $\sum \cos$ and $\csc$ equivalent?

Published on 13 Apr 2026 - 18:36

score 138 · Answer 6 · 2026-04-15 21:11:40

138

Views

Find the value of $\sin(\tfrac{\pi}3) + \tfrac12\sin(\tfrac{2\pi}3) + \tfrac13\sin(\tfrac{3\pi}3)+\dots$ up to infinity

Published on 15 Apr 2026 - 21:11

score 168 · Answer 7 · 2026-04-10 19:57:30

168

Views

Does this formula for a sum of cosines has a name?

Published on 10 Apr 2026 - 19:57

score 102 · Answer 8 · 2026-05-10 13:50:48

102

Views

Subtle Carefulness in use of AM-GM inequality

Published on 10 May 2026 - 13:50

score 40 · Answer 9 · 2026-04-16 14:34:09

40

Views

Trig Sequence Puzzel?

Published on 16 Apr 2026 - 14:34

score 52 · Answer 10 · 2026-04-29 12:27:24

52

Views

Equivalence between $\phi (z,s,a)$ and a sum of single impulses

Published on 29 Apr 2026 - 12:27

score 167 · Answer 11 · 2026-04-16 22:57:10

167

Views

Sine series: angle multipliers add to 1

Published on 16 Apr 2026 - 22:57

score 90 · Answer 12 · 2026-04-16 03:04:26

90

Views

Limiting Behavior of the oscillating series

Published on 16 Apr 2026 - 3:04

score 209 · Answer 13 · 2026-04-16 13:23:51

209

Views

$\frac{1}{n}-\sin(\frac{1}{n})\sim\frac{1}{6n^3}$?

Published on 16 Apr 2026 - 13:23

score 125 · Answer 14 · 2026-04-14 02:12:31

125

Views

Sum of sines inequality

Published on 14 Apr 2026 - 2:12

score 90 · Answer 15 · 2026-04-16 15:08:44

90

Views

Prove that $\tan^{-1}(1/n)+\tan^{-1}(2/n)+\cdots+\tan^{-1}(n/n)$ increases as $n$ increases

Published on 16 Apr 2026 - 15:08

List Question

Simplify $\sin(\alpha)+\sin(\alpha+x)+\sin(\alpha+2x)+\sin(\alpha+3x)+ \dotsb +\sin(\alpha+nx)$

Convergent series with trigonometric functions like $a_{0}=m, a_{2n-1}=\sin(a_{2n-2}), a_{2n}=\cos(a_{2n-1})$

Proving a general formula for $\sum_{m=0}^{n}(-1)^m\binom{n}{m} \sin(a+(n-m)h)$

For rotation matrix $A$, find $B = A^4- A^3 + A^2 - A$

Why are these $\sum \cos$ and $\csc$ equivalent?

Find the value of $\sin(\tfrac{\pi}3) + \tfrac12\sin(\tfrac{2\pi}3) + \tfrac13\sin(\tfrac{3\pi}3)+\dots$ up to infinity

Does this formula for a sum of cosines has a name?

Subtle Carefulness in use of AM-GM inequality

Trig Sequence Puzzel?

Equivalence between $\phi (z,s,a)$ and a sum of single impulses

Sine series: angle multipliers add to 1

Limiting Behavior of the oscillating series

$\frac{1}{n}-\sin(\frac{1}{n})\sim\frac{1}{6n^3}$?

Sum of sines inequality

Prove that $\tan^{-1}(1/n)+\tan^{-1}(2/n)+\cdots+\tan^{-1}(n/n)$ increases as $n$ increases

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