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A sum of Cosines (Fouries series)

  1. Dec 1, 2011 #1
    Dear All,

    I wonder how to calculate the sum of the following Cosines:
    \sum_{n=1}^\infty \cos(nx)

    Can anyone give a hint? Thanks a lot!
  2. jcsd
  3. Dec 1, 2011 #2
    First, use the following formula:

    [tex]\cos \alpha= \frac{e^{i\alpha}+e^{-i\alpha}}{2}.[/tex]

    Then apply formulas of geometric series.
  4. Dec 1, 2011 #3


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    A little simpler is to directly compute

    [tex] \sum_{n=1}^{\infty} (\cos nx + i\sin nx) [/tex]

    and at the end separate the real and imaginary parts. Also gives you the sume of sines.
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