For the following sum:
$\cos(2\theta) + \cos^2(2\theta) + \cos^3(2\theta) ...+ \cos^N(2\theta)$
Why is the range $\{0 < \theta <\frac{\pi}{2}\}$ for there to be a sum?
2026-03-30 02:10:14.1774836614
Geometric sequences with trigonometry
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There is no restriction on the range for there to be a sum. For example if $\theta=\pi$ then the sum is $N$, or if $\theta=\pi/2$ then the sum is -1 or 0 depending on whether $N$ is odd or even. There isn't any value of $\theta$ where the sum is not defined.