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Infinite sum

  1. Sep 16, 2008 #1
    [tex]\sum{a^ncos(nx)}[/tex]

    from zero to infinity

    a is a real number -1 < a < 1

    I rewrote this as a geometric series involving a complex exponential

    Real part of

    [tex]\sum{(ae^{ix})^n}[/tex]

    Which is a geometric series with common ratio r < 1, so it converges to the sum

    (first term)/(1-r)

    which seems to be

    [tex]\frac{1}{1-ae^{ix}}[/tex]

    taking the real part and multiplying top and bottom by (1-acosx), I get


    [tex]\frac{1-acos(x)}{1-2acos(x) + a^2cos^2(x))}[/tex]

    which is different from the desired result of

    [tex]\frac{1-acos(x)}{1-2acos(x) + a^2)}[/tex]

    Any help would be appreciated
     
  2. jcsd
  3. Sep 16, 2008 #2
    From this point on this go wrong...
     
  4. Sep 16, 2008 #3
    I know i've gone wrong somewhere. I'd like to know what I did wrong.
     
  5. Sep 16, 2008 #4
    First work out the fraction then take the imaginary part.
     
  6. Sep 16, 2008 #5
    Got it. Thanks.
     
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