How to solve sum of \cos(kx) for the case \cos(x)=1I have the solution for \sum^

Reginald Metcalf

Reginald Metcalf

Answered question

2022-01-17

How to solve sum of cos(kx) for the case cos(x)=1
I have the solution for {k=1}ncos(kx):
k=1ncos(kx)=R(k=1neikx)
=R(eixeinx1eix1)=R(eixeinx2eix2einx2einx2eix2eix2)=R(ei(n+1)x2sinnx2sinx2)=sinnx2sinx2cos((n+1)x2)
but if eix=1 i am dividing trough 0 in line 2. So i know that in this case eix1. So my question is: What is the k=1ncos(kx)  if  eix=1

Answer & Explanation

Mollie Nash

Mollie Nash

Beginner2022-01-18Added 33 answers

eix=1 means x=2mπ with mN. And in that case the sum you’re looking for is equal to n.

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