如何通过以下三个式子估计pi的值？

Question

因为我需要找到每个式子与pi的差来画图，但是根本没懂要怎么找到他们与pi的关系。

Answer 1

import math

def One(n):
    fun = 1
    for i in range(1, n + 1):        
        t = 4 * i ** 2
        fun *= t / (t - 1)
    return fun * 2

def Two(n):
    fun = 0
    for i in range(0, n + 1):
        t1 = 2 ** i * math.factorial(i) ** 2
        t2 = math.factorial(2 * i + 1)
        fun += t1 / t2
    return fun * 2

def Three(n):
    fun = 0
    for i in range(1, n + 1):
        t1 = (-1) ** (i + 1)
        t2 = i * (i + 1) * (2 * i + 1)
        fun += t1 / t2
    return fun + 3

n = 100
pi1 = One(n)
pi2 = Two(n)
pi3 = Three(n)
print(pi1, pi2, pi3)