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)
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.