Basel_rapid.py

# Basel problem, converges rapidly
# Calculates with wanted number precision
# Juhani Kaukoranta 23.6.2018

from decimal import *
import math


def binomial(n,k):
    a = math.factorial(n)//(math.factorial(n-k)*math.factorial(k))
    return(a)

def Basel(precision):
    getcontext().prec=precision
    b = Decimal(0)
    for n in range(1,2*precision):
        b = b+Decimal(1)/(n*n*binomial(2*n,n))
    return(3*b)
precision = int(input("How many numbers precision, f.eq 100 "))
print("Basel problem = ",Basel(precision))
print("Pi^2/6 = ",math.pi*math.pi/6)