import numpy as np
import matplotlib.pyplot as plt

def trekant(x):
	if x < 0:
		return x + np.pi
	else:
		return np.pi - x

def partialsum(x,N):
	S = np.pi/2
	for n in range(N):
		S += 4*np.cos((2*(n+1)-1)*x)/(np.pi*(2*(n+1)-1)**2)
	return S

x = np.linspace(-np.pi, np.pi, 1000)
y = [trekant(t) for t in x]
y1 = [partialsum(t,100) for t in x]

fig, ax = plt.subplots()

ax.plot(x,y)
ax.plot(x,y1)

ax.grid(True)

ax.spines['left'].set_position('zero')
ax.spines['bottom'].set_position('zero')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')

plt.show()