My question wants me to derive the equality /4 = 1 - 1/3 + 1/5 - 1/7... using the Fourier Series:
4/ ∑ 1/(2n+1)sin((2n+1)x) = -1 if -1 < x < 0
1 if 0 < x < 1
To me it looks like the Fourier Sine expansion of f(x) = 1 with an odd extension, but where does the sin(nx) disappear to?