# -*- coding: utf-8 -*-
"""
Created on Fri Jun 28 16:40:33 2024

@author: franc
"""

import math
import matplotlib.pyplot as plt


# Question 1
def u(n):
    v=1
    for k in range(1,n+1):
        v*=1-1/(4*k**2)
    return v

print()
print()
        
for n in range(1,11):
    print(u(n))
    
print()
print()
for k in range(1,5):
    print(1/u(10**k))
    
print()
print('valeur de pi/2=',math.pi/2)
    
 
# Question 2.b.
def f(t):
    s=0
    for k in range(1,101):
        s+=2*t/(t**2-k**2*math.pi**2)
    return s
    
def g(t):
    return math.cos(t)/math.sin(t)-1/t
    
lx=[k/100 for k in range(1,300)]
ly=[f(x) for x in lx]
lz=[g(x) for x in lx]
plt.plot(lx,ly)
plt.plot(lx,lz)   
""" Il semblerait que les deux courbes se superposent"""