# Fourier series

## Homework Statement

Compute the Fourier series for the given function f on the specified interval
f(x) = x^2 on the interval − 1 < x < 1

## The Attempt at a Solution

Just wondering if anyone can verify my answer?

f(x)=1/3+$$\sum$$(4/(n^2*pi^2)*(-1)^n*cos(n*pi*x))

## The Attempt at a Solution

Cyosis
Homework Helper
Yep that is correct.

cheers

the next part of the question says to determine if the function to which the fourier series for f(x) converges?? does this make sense to anyone?

Cyosis
Homework Helper
Is that exactly how the question is asked in your text? The "if" confuses me. I guess what they are asking you is if the Fourier series you just derived converges. Which is pretty easy to show.

how do you show that it converges?? just pick example numbers??

Cyosis
Homework Helper
That would mean you would have to pick an infinite amount of numbers though. To show that it converges compare it to a series you know to be convergent. For example, $\sum_{n=1}^\infty \frac{1}{n^2}$. You could also try the root test and or ratio test.

jbunniii
That would mean you would have to pick an infinite amount of numbers though. To show that it converges compare it to a series you know to be convergent. For example, $\sum_{n=1}^\infty \frac{1}{n^2}$. You could also try the root test and or ratio test.