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Homework Help: Sequences and Series of Functions

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Let sum of a sub k
    be an absolutely convergent series.

    a. Let f be the function defined by f(x) = sum of (a sub k) * sin(kx). Prove that:

    the integral from 0 to pi/2 of f = sum of (a2k-1 + a4k-2)/(2k-1)
    2. Relevant equations

    I already showed that f(x) converges uniformly using the Weirstrass M theorem

    3. The attempt at a solution

    I'm completely stuck. I understand convergence of sequences and proving uniform continuity of sequences, but when we begin to use the summation with the sequence of functions, I am totally lost. Any help would be greatly appreciated.
     
  2. jcsd
  3. Apr 12, 2010 #2

    lanedance

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    Homework Helper

    have you tried evaulating the integral explicitly?
     
  4. Apr 12, 2010 #3

    lanedance

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    Homework Helper

    also to write in tex see below
    [tex] \int^{\pi/2}_0 dx f = \int^{\pi/2}_0 dx \sum a_k sin(kx)[/tex]
     
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