find_pi_to_the_nth_digit.py

#coding:utf-8
"""
Pi = SUM k=0 to infinity 16^-k [ 4/(8k+1) - 2/(8k+4) - 1/(8k+5) - 1/(8k+6) ]
ref: https://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml
"""
from __future__ import division
import math
from decimal import Decimal as D
from decimal import getcontext


getcontext().prec = 400
MAX = 10000
pi = D(0)


for k in range(MAX):
    pi += D(math.pow(16, -k)) * (D(4/(8*k+1)) - D(2/(8*k+4)) - D(1/(8*k+5)) - D(1/(8*k+6)))

print 'PI >>>>>>>>>>' , pi