The partial sums sn(x) of a Fourier series show oscillations near a discontinuity point. These oscillations do not disappear as n increases but instead become sharp "spikes". They were explained mathematically by J.W Gibbs3. Graph sn(x) in Prob. 10. When n = 50, say, you will see those oscillations quite distinctly. Consider other Fourier series of your choice in a similar way. Compare.