如何用Python手写一个PI计算器（3.14，pi节）

import math
from math import factorial as fac

def calc_pi(k):
    '''
    1/pi =  2\sart(2)/9801 \dot
            \sum_{n=0}^{\infinity} \{ 
                \frac{(4n)!}{(n!)^4} \dot
                \frac{26390n+1103}{(396)^{4n}}
            \}
    -- by Ramanujan 1910
    '''
    const = 2*math.sqrt(2)/9801
    sum = 0
    n=0
    while n<=k:
        sum+=fac(4*n)/math.pow(fac(n),4)*(26390*n+1103)/math.pow(396,4*n)
        n+=1
    sum = const*sum
    return 1/sum


if __name__=="__main__":
    for k in range(0,2):
        pi = calc_pi(k)
        print(f"{k}: {pi}")