Fourier series help?

Question

What does the Fourier sine series for f(x)=x^2 is on (0,Pi)? Can you please explain your steps? Also, what does the series converge to at x=Pi? thx in advance!:)

Answer 1

Computing the coefficients involves integration by parts. It's a grind.

As for the second question, every term will involve sine of an integer multiple of pi, so you can figure our what the sum converges to without even finding the coefficients.