Based on Fourier series, a rectangle wave with a period of can be approximated mathematically by a sum of sin functions as,

() = sin() + sin(3) 3 + sin(5) 5 + sin(7) 7 + + sin()

Where the approximation become closer to the rectangle wave by increasing k (or the total number of terms n). 1) Write a function coefficient with two parameters: n representing the number of Fourier series terms, and a NumPy array x for x values in range -5 to 5. This function should return a NumPy array with the corresponding function f(x) or y.

Hint: note that k = 2*n-1.

2) Use this function to plot in one figure 4 subplots, for n =1, n = 4, n = 20, n = 100 respectively. Include n value each subplot legend. Use different colour/marker for each subplot. Label each horizontal axis as X and each vertical axis as Y. Add tickets with at -, 0 and horizontal positions. Notes: you can use $\pi$ to display symbol. In case of overlapping labels, you can use plt.tight_layout()

3) What is the range in each subplot, i.e. maximum f(x) value minimum f(x) value.