#!/usr/bin/python3

import math

def bailey_borwein_plouffe_pi(n):
	result = 0
	for k in range(n):
		result += (1/16)**k * ( 4/(8*k + 1) - 2/(8*k + 4) - 1/(8*k + 5) - 1/(8*k + 6))

	return result

if( __name__ == "__main__"):

	assert bailey_borwein_plouffe_pi(1000) == math.pi