from math import sqrt
def f(x) :
    return (sqrt(1+x**2))

def petits_rectangles(n):
    s=0
    for k in range (n):
        s=s+(1/n)*f(k/n)
    return s

def grands_rectangles(n):
    S=0
    for k in range (1,n+1):
        S=S+(1/n)*f(k/n)
    return S

def encadrement(n):
    s=petits_rectangles(n)
    S=grands_rectangles(n)
    return (s,"<I<",S)

print (encadrement(1000))