from random import randint

def simulation():
    compteur = 0

    for i in range(30):
        a = randint(1, 6)
        b = randint(1, 6)

        if a > b:
            resultat = a
        else:
            resultat = b

        if resultat == 5:
            compteur = compteur + 1

    return compteur

print(simulation())

##
from random import randint

def frequence():
    compteur = 0

    for i in range(30):
        a = randint(1, 6)
        b = randint(1, 6)

        if a > b:
            resultat = a
        else:
            resultat = b

        if resultat == 4:
            compteur = compteur + 1

    return compteur / 30

print(frequence())

##
def somme(n):
    S = 0

    for k in range(1, n + 1):
        S = S + ((-1)**(k + 1)) / k

    return S

print(somme(10))

##
def somme(n):
    S = 0

    for k in range(1, n + 1):
        S = S + ((-1)**(k + 1)) / k

    return S

print(somme(10))
print(somme(100))
print(somme(1000))
print(somme(10000))

##
def n_eme_terme(r, n):
    u = r

    for i in range(n):
        u = ((-1)**i) * u + 2

    return u

print(n_eme_terme(-100, 5))

##
def moyenne(r, n):
    total = 0

    for i in range(n):
        total = total + n_eme_terme(r, i)

    return total / n

print(moyenne(-100, 20))

##
def plus_grand(r, n):
    maximum = n_eme_terme(r, 0)

    for i in range(1, n):
        u = n_eme_terme(r, i)

        if u > maximum:
            maximum = u

    return maximum

print(plus_grand(-100, 20))

##
def moyenne(r, n):
    total = 0

    for i in range(n):
        total = total + n_eme_terme(r, i)

    return total / n

print(moyenne(-100, 20))

##
def plus_grand(r, n):
    maximum = n_eme_terme(r, 0)

    for i in range(1, n):
        u = n_eme_terme(r, i)

        if u > maximum:
            maximum = u

    return maximum

print(moyenne(-100, 20))