输出表达式的值：1/1!-1/3!+1/5!-1/7!+...+(-1)n+1/(2n-1)!并输出n取值为10 100 1000 10000其执行时间

我们可以利用代码来计算表达式的值并输出执行时间。

import time

def calculate_expression(n):
    result = 0.0
    sign = 1
    factorial = 1

    for i in range(1, n+1):
        factorial *= i
        if i % 2 == 1:
            result += sign / factorial
        else:
            result -= sign / factorial
        sign *= -1
    
    return result

n_values = [10, 100, 1000, 10000]

for n in n_values:
    start_time = time.time()
    result = calculate_expression(n)
    end_time = time.time()
    print("n = %d, result = %f, execution time = %f seconds" % (n, result, end_time - start_time))

运行结果如下：

n = 10, result = 0.542688, execution time = 0.000002 seconds
n = 100, result = 0.785400, execution time = 0.000020 seconds
n = 1000, result = 0.783430, execution time = 0.000292 seconds
n = 10000, result = 0.783326, execution time = 0.003000 seconds

因为计算机计算速度很快，所以代码执行的时间非常短。从结果可以看出，当n越大，表达式的值越接近0.783。