Tagged Questions
7
votes
1answer
91 views
Need help with calculating this sum: $\sum_{n=0}^\infty\frac{1}{2^n}\tan\frac{1}{2^n}$
I need help with calculating this sum:
$$\sum_{n=0}^\infty\frac{1}{2^n}\tan\frac{1}{2^n}$$
5
votes
1answer
66 views
finding $\lim_{n\rightarrow\infty}\sum_{r=1}^{n}\arctan\left(\frac{2r}{1-r^2+r^4}\right)$
I want to find
$$L=\lim_{n\rightarrow\infty}\sum_{r=1}^{n}\arctan\left(\frac{2r}{1-r^2+r^4}\right)$$
I already know that I need to split the expression $\frac{2r}{1-r^2+r^4}$ of the form ...
2
votes
2answers
171 views
Power Reducing Formula
I need some how with the power reducing formula. I'm having trouble understanding how to apply it. Here's an equation that utilizes it:
$\cos^2 (\theta x) - 1 = 0$
How do I solve this on the ...
1
vote
1answer
70 views
Trigonometry Identities
Consider a collection of five points evenly spaced around a circle to form a regular
pentagon. Assume the figure is scaled so that the sides of the pentagon have length 1.
Question: Use Ptolemy’s ...
0
votes
1answer
53 views
trigonometric summation
Taking into consideration the functions
$$\sum_{t=0}^{n} \sin{(\theta + t \phi)}=\frac{\sin({\frac{(n+1)\phi}2})\sin{(\theta+\frac{n \phi}2)}}{\sin{(\frac{\phi}2)}}$$
and
...
6
votes
2answers
175 views
Calculate: $\sum_{k=0}^{n-2} 2^{k} \tan \left(\frac{\pi}{2^{n-k}}\right)$
Calculate the following sum for integers $n\ge2$:
$$\sum_{k=0}^{n-2} 2^{k} \tan \left(\frac{\pi}{2^{n-k}}\right)$$
I'm trying to obtain a closed form if that is possible.
