Sequences and Series of Functions

  • Thread starter Fiz2007
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  • #1
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Homework Statement



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)

Homework Equations



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

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.
 

Answers and Replies

  • #2
lanedance
Homework Helper
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2
have you tried evaulating the integral explicitly?
 
  • #3
lanedance
Homework Helper
3,304
2
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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