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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 (a

_{2k-1}+ a

_{4k-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.