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Homework Help: Fourier Series

  1. Apr 3, 2009 #1
    Find the fourier expansion of one period of f(t)=1+t absolute value of t<1

    I found this to be 1+2/pi Sigma(0 to infinity) ((-1^(n+1))/n)sinnpit by just the standard methods of the a0 an and bn formuals, which I know is correct

    Now the parts I am having problems with is part b and c which our teacher has not covered much at all and I cannot find any help online.

    Part b. Use the fourier expansion of f to find the sum of the Series

    Part C. If f denotes the function defined on (-infinity to infinity) by the fourier series of f, find F(1)+F(-5)-3F(0)
  2. jcsd
  3. Apr 3, 2009 #2
    Just to make things a bit more clear on the notation side, I take it your expansion is:

    [tex]1+\frac{2}{\pi}\sum_{n=0}^{\infty}\frac{(-1)^{n+1}}{n} \sin{n\pi t}[/tex]

    As for question b:

    Notice that if you set t equal to [tex]t_0 \equiv \frac{1}{2}[/tex], then

    [tex]\sin{n\pi t_0} = \sin{\frac{n\pi}{2}}[/tex]

    which is zero whenever n is even and [tex](-1)^{(n-1)/2[/tex] whenever n is odd.... Do you see where I'm going with this?

    part C:
    I take it by F(0) you just mean f(0)? Have you tried filling in these numbers into the fourier series?
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