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Fourier Series- half range sine series

  1. Nov 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Let f(x)=x, 0≤x≤p

    (a.) Compute the half-range sine series
    (b.) Use the series to show that 1-(1/3)+(1/5)+...=π/4


    2. Relevant equations

    bn=(2/L)*int(from 0 to L) f(x)*sin(nπx/L) dx

    3. The attempt at a solution

    bn=(2/p)*int(from 0 to p) x*sin(nπx/p) dx

    Using integration by parts I get:

    bn= 2[(-p*cos(nπ)/nπ) + (p*sin(nπ)/n2π2)]

    I'm not really sure where to go from here, any help is appreciated.
     
  2. jcsd
  3. Nov 6, 2012 #2

    vela

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    Since n is an integer, you can simplify ##\cos n\pi## and ##\sin n\pi##.
     
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