import math
# 公式一：e ≈ (1 + 1/n)^n
def calculate_e_formula1(n):
    return (1 + 1 / n) ** n
# 公式二：e ≈ Σ（从k=0到n）1/k!
def calculate_e_formula2(n):
    e = 0
    factorial = 1  # 用于计算阶乘，初始为0! = 1
    for k in range(n + 1):
        if k == 0:
            factorial = 1
        else:
            factorial *= k
        e += 1 / factorial
    return e
# 测试，取n = 1000
n = 1000
e_formula1 = calculate_e_formula1(n)
e_formula2 = calculate_e_formula2(n)
print("公式一计算结果：", e_formula1)
print("公式二计算结果：", e_formula2)
print("Python 内置 math.e 值：", math.e)

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