First few truncated Fourier series for the triangular pulse f(x) of period 2pi, with f(x)=|x| for -pi<x<pi.

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1/2*Pi-4*cos(x)/Pi

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1/2*Pi-4*cos(x)/Pi-4/9*cos(3*x)/Pi

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1/2*Pi-4*cos(x)/Pi-4/9*cos(3*x)/Pi-4/25*cos(5*x)/Pi

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1/2*Pi-4*cos(x)/Pi-4/9*cos(3*x)/Pi-4/25*cos(5*x)/Pi-4/49*cos(7*x)/Pi