#!/usr/bin/env python3

-- coding: utf-8 --

import itertools

def pi(N):

# step 1
ns = itertools.count(start=1, step=2)
# step 2
ns = itertools.takewhile(lambda x: x <= 2*N-1, ns)
# step 3
L = []
for i in ns:
    L.append((-1)**((i+1)/2%2+1)*4/i)
# step 4
return sum(L)

if name == 'main': print(pi(10)) print(pi(100)) print(pi(1000)) print(pi(10000)) assert 3.04 < pi(10) < 3.05 assert 3.13 < pi(100) < 3.14 assert 3.140 < pi(1000) < 3.141 assert 3.1414 < pi(10000) < 3.1415 print('ok')