def factorial(n):
    result = 1
    while n > 1:
        result *= n
        n -= 1
    return result

def e1(iterations):
    result = 0
    for k in range(iterations):
        result += 1.0 / factorial(k)
    return result

def e2(iterations):
    result = 0
    factorial = 1
    for k in range(1, iterations + 1):
        result += 1.0 / factorial
        factorial *= k
    return result
    

print(e2(110))

print(e1(100))