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Fourier series

  1. May 8, 2016 #1
    1. The problem statement, all variables and given/known data
    the answer that i get is different with the answer provided , is my answer wrong ? i got ( cos(2n -1) / 2n-1 )instead of ( cos(n+1) / n+1 )

    2. Relevant equations

    3. The attempt at a solution
    Last edited by a moderator: May 8, 2016
  2. jcsd
  3. May 8, 2016 #2


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    It's easy enough to check yourself. Try plotting each series. You only need 4 or 5 terms each.

    www.desmos.com is useful if you don't have access to plotting software.
  4. May 9, 2016 #3
    I am not interested in the graph, I just wanna know the final answer....
  5. May 9, 2016 #4


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    I actually followed vela's good advice, and the result is telling ...

    Another test you could try: what happens with the given solution (answer b) when x=π?
    Last edited: May 9, 2016
  6. May 9, 2016 #5
    Cos(n +1 ) pi= (-1)^n.... What can we conclude from that??
  7. May 9, 2016 #6


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    No, that is not correct.
    ##\cos 2 \pi = \cos (1+1) \pi \neq {(-1)}^1##

    Once you have the correct values, plug them in into the Fourier series of answer (b).
  8. May 9, 2016 #7
    It's (-1) ^ (n +1)
  9. May 9, 2016 #8


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    So what is the Fourier series of answer (b) for x=π? Does it converge? If so, to what value?

    And don't forget about vela's advice: it takes 2 minutes, and yields very interesting information.
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