# Sequences and Series of Functions

## 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

Related Calculus and Beyond Homework Help News on Phys.org
lanedance
Homework Helper
have you tried evaulating the integral explicitly?

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