NEED PYTHON CODE PLEASE! Power series aren't the only way to write a function as an infinite sum of simpler terms! Depending on your choice of engineering major, you'll come across Fourier series, which are infinite sums of sines and cosines that represent periodic functions $($functions that repeat their values at regular intervals$).$ This is especially useful in acoustics.

Here is one common example, the square wave $f(x)=4{|}_{{?}_{?}}{x}_{{?}_{?}}|-2{|}_{{?}_{?}}2x_{{?}_{?}}|+1($for any $t$ that isn't a multiple of $\frac{1}{2}),$ where ${|}_{{?}_{?}}{*}_{{?}_{?}}|$ is the floor function $($round down the inside$).$ It can be represented by the Fourier series:

$\frac{4}{}{\displaystyle \underset{k=1}{\overset{}{}}}\frac{1}{2k-1}sin(2(2k-1)x).$

$($a$)$ Compute the first $5$ partial sums of this series.

$($b$)$ Plot the square wave along with its first $5$ partial sums on the same graph, with $x-$domain $0,2.$ Use sp$.$floor for the floor parts of the wave function.