Fourier Series with Mathematica

We should probably not tell about this as it is important to compute Series by hand at first. Here are examples: 

FourierSinCoefficient[Sign[x], x, 10]
FourierCosSeries[Abs[Sin[3 x]], x, 20]
FourierSinSeries[Sign[x], x, 10]                                        
FourierTrigSeries[If[x<0,0,1], x, 20]
From Spring 2017, a poem found by the computer by Jorma Goerns: 
 
He rose passionately
To tackle today's PSET
But then he thought eventually
"Oh, I should have stayed in bed!"

A golden sun was shining
His motivation dying
This function's Fourier series
Remained oh so mysterious!

A deafening cry: Eureka!
Am I not a genius?
He opened Mathematica
And found the Fourier series.