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Consider the function f ( x ) = 4 π ( cos ⁡ x 1 −...

Consider the function LaTeX: f(x)=\frac{4}{\pi}\left(\frac{\cos x}{1}-\frac{\cos 3x}{3}+\frac{\cos 5x}{5}-\frac{\cos 7x}{7}+\cdots \right) f ( x ) = 4 π ( cos ⁡ x 1 − cos ⁡ 3 x 3 + cos ⁡ 5 x 5 − cos ⁡ 7 x 7 + ⋯ ). Fire up a plotting program or spreadsheet, and plot this over the range of x=0 to 4π. Do it one term at a time, so make four plots: one with the first term, one with the first and second, the next with one, two, and three, and the last with all four. What shape is this converging on?

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On adding more and more terms it is converging towards the square wave, all the plots are

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