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5
questions with no upvoted or accepted answers
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How to solve $\sum_{n=-\infty}^\infty\frac{y^2}{[(x-n\pi)^2+y^2]^{3/2}}$?
I need to solve this sum:
$$\sum_{n=-\infty}^\infty\frac{y^2}{[(x-n\pi)^2+y^2]^{3/2}}.$$
Do you have any ideas for how I could do this?
I know that this sum:
$$\sum_{n=-\infty}^\infty\frac{y}{(x-n\pi)^...
- 1,027
1
vote
1
answer
194
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Trigonometric Identities Using De Moivre's Theorem
I am familiar with solving trigonometric identities using De Moivre's Theorem, where only $\sin(x)$ and $\cos(x)$ terms are involved. But could not use it to solve identities involving other ratios. ...
1
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0
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487
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A generalised formula for $\cos {n\theta}$ in terms of powers of $\cosθ$ using De Moivre's Theroem
I am trying to generalise a formula for $\cos{nθ}$ in terms of powers of $\cosθ$ using De Moivre's Theorem for a high school assignment.
The equations are here:
I was wondering if letting $m= ⌊n/2⌋-j+...
- 101
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votes
1
answer
78
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Summation of an Infinite Series involving Trigonometry
I came across this summation problem the other day and I am not quite sure how to approach it
$$S=\sum_{n=0}^{n=\infty}\frac{2^{n-1}}{3^{2n-2}}\sin\left(\frac{\pi}{3.2^{n-1}}\right)$$
My approach ...
- 1,292
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votes
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How to prove this quasi-geometric trigonometric series identity without induction
$$\frac{2}{\sin{x}}\sum_{r=1}^{n-1} \sin{rx}\cos{[(n-r)y]} \equiv \frac{\cos{(nx)}-\cos{(ny)}}{\cos{x}-\cos{y}} - \frac{\sin{(nx)}}{\sin{x}}$$
The identity can be tediously proven using the Axiom of ...
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