def ex2_rec(n):
    if n == 0:
        return 0
    return 2*ex2_rec(n-1) + 3**n

def ex2_fechada(n):
    return (-3)*(2**n) + 3**(n+1)

def ex3_rec(n):
    if n == 0:
        return 0
    return 2*(ex3_rec(n-1)) + 2**n

def ex3_fechado(n):
    return n * (2**n)

def ex4_rec(n):
    if n == 0:
        return 3
    if n == 1:
        return 6
    return 4*ex4_rec(n-1) - 4*ex4_rec(n-2) + 2**n

def ex4_fechado(n):
    return 2**(n-1) * (n**2 - n + 6)

def verifica(até,fun1,fun2):
    for n in range(até+1):
        print(f"{n} ... {fun1(n) == fun2(n)}")