Question

How to prove $\sum_{k=1}^{N} \frac{\sin n\theta}{2^N}=\frac{2^{N+1}\sin \theta + \sin N\theta -2\sin(N+1)\theta}{2^N(5-4\cos \theta)}$

score 846 · Answer 1 · 2026-04-24 02:14:32

846

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How to prove $\sum_{k=1}^{N} \frac{\sin n\theta}{2^N}=\frac{2^{N+1}\sin \theta + \sin N\theta -2\sin(N+1)\theta}{2^N(5-4\cos \theta)}$

Published on 24 Apr 2026 - 2:14

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3.7k

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193

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score 344 · Answer 15 · 2026-04-15 23:19:02

344

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If f is analytic in the unit disk and $|f(z)|\leq \frac{1}{1-|z|}$ then $|f'(0)|\leq 4$

Published on 15 Apr 2026 - 23:19

List Question

How to prove $\sum_{k=1}^{N} \frac{\sin n\theta}{2^N}=\frac{2^{N+1}\sin \theta + \sin N\theta -2\sin(N+1)\theta}{2^N(5-4\cos \theta)}$

$z^5=-2$ Complex number solutions

Why left eigenvector complex conjugate transpose of right eigenvector?

If $|z +\frac{1}{z}|=a$ find extreme values of $|z|$

How does a complex exponential turn into the sinc function?

How to find vertices of square in complex numbers

How to solve $z^2\overline z-z\overline z=-\overline z$

Find the minimum $n$ such that $z^n\in(-\infty,0)$

solution of $\bar{z}=\xi z$

Sign of the real part of two complex numbers

Complex numbers in my system of equations

What is $\sqrt{-i}$

An iterative sequence of complex numbers

Write in $a+ib$ form the following number $\cos ( \frac{\pi}{3} + iLog(4))$

If f is analytic in the unit disk and $|f(z)|\leq \frac{1}{1-|z|}$ then $|f'(0)|\leq 4$

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