# -*- coding: utf-8 -*-
"""
Exercice 1-6 : Sommes partielles d'une série de Fourier
Created on Mon May 23 14:11:22 2016

@author: grivet
"""

import numpy as np
import matplotlib.pyplot  as plt
Pi = np.pi

def un(n, x):
    return (-1)**n*np.cos((2*n+1)*x)/(2*n+1)

def sn(N, x):
    s = 0
	#  i = 0,1,...,N
    for i in range(N+1):
        s += un(i, x)
#        print(i)
    return s

t = np.linspace(-Pi, 2*Pi, 200)
plt.plot(t, sn(3, t),label="n = 3")
plt.plot(t, sn(4, t),label="n = 4")
plt.plot(t, sn(6, t),label="n = 6")
plt.plot(t, sn(10, t),label="n = 10")

plt.legend(loc="best")