#!/usr/bin/env python3
# -*- encoding: utf-8 -*-
import itertools

def pi(N):
    natuals = itertools.count(1, 2)
    ns = list(itertools.takewhile(lambda x: x < 2 * N, natuals))
    ops = itertools.cycle([1, -1])
    sum = 0
    count = 0
    for op in ops:
        sum += 4 / ns[count] * op
        count += 1
        if count == N:
            break

    return sum






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')