Find the Fourier series of f(x)=−5∣x∣+1 on the interval [−1,1]. That is, find the numbers a₀,aₖ, and bₖ (where ak and bk may depend on k )such that
f(x)=a₀ +∑k=1[infinity](aₖ cos(πkx)+bₖ sin(πkx))
for all x with −1