Solve Fourier Sine Series - Get Help Here!

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SUMMARY

The forum discussion centers on solving Fourier Sine Series, specifically the simplification of coefficients denoted as ##b_n##. Users clarify that for odd values of ##n##, the coefficients simplify to 0, while even values yield different results. The conversation highlights the importance of recognizing identities in Fourier analysis to arrive at the final solution. Participants express gratitude for assistance and share insights on the problem-solving process.

PREREQUISITES
  • Understanding of Fourier Series concepts
  • Familiarity with trigonometric identities
  • Basic knowledge of series convergence
  • Experience with mathematical notation and simplification techniques
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  • Study the properties of Fourier Sine Series
  • Learn about convergence criteria for Fourier series
  • Explore trigonometric identities relevant to Fourier analysis
  • Practice problems involving the simplification of Fourier coefficients
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Students and educators in mathematics, particularly those focusing on Fourier analysis, as well as anyone seeking to deepen their understanding of series and trigonometric simplifications.

AerospaceEng
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Everything is in the picture I've attached. I believe my work is right because it's not that difficult of a problem but what I'm having a hard time seeing is how i go from the coefficient bn that I've calculated to the final solution. Maybe I did screw up or maybe there's an identity I'm not seeing.

Anyways if anyone is able to help that would be greatly appreciated thanks! :D

Problem.jpg

 
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What does ##b_n## simplify to if ##n## is odd?
 
Hey Jbuns Thanks so much I see how odd n's simplify to 0 and how the the terms simplify when n is even. Also thank you for your post on my other question. If you ever need anything! hit me up lol :D
 

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