# -*- coding: utf-8 -*-
"""
Created on Fri Jun 14 20:12:08 2024

@author: franc
"""

import math

# Question 1.
def f(x):
    return 1/math.sqrt(2)*math.sqrt(1-math.sqrt(1-x**2))
    

def x(n):
    if n==0:
        return 0.5
    else:
        return f(x(n-1))
        

def u(n):
    return 6*2**n*x(n)
    
def uprime(n):
    return (4*u(n+1)-u(n))/3

print()
print()
print('sept premières valeurs de u(n)')
for k in range(7):
    print(u(k))
    
print()
print()
print('sept premières valeurs de uprime(n)')

for k in range(7):
    print(uprime(k))
    
print()
print()
print('valeur du nombre pi')
print(math.pi)