Evaluate the sum of the infinite series 1+cos⁡x+cos2x+cos3x… for 0<x<π Therefore ∑n=0∞cosnx which is just...

Emmy Combs

Emmy Combs

Answered

2022-01-26

Evaluate the sum of the infinite series 1+cosx+cos2x+cos3x for 0<x<π
Therefore n=0cosnx
which is just a geometric series with common ratio cosx and first term 1. So the sum of the series should be
n=0cosnx=11cosx
However, the answer to the question is 12csc2(x2)

Answer & Explanation

becky4208fj

becky4208fj

Expert

2022-01-27Added 10 answers

You did the right thing. Then you make use of the fact that
1cos(x)=1(cos2(x2)sin2(x2)) 
=2sin2(x2)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?