def pi(N): n = itertools.count(1)

#' 计算pi的值 '
# step 1: 创建一个奇数序列: 1, 3, 5, 7, 9, ...
odd_number = itertools.takewhile(lambda x: x < 2*N, n)
# step 2: 取该序列的前N项: 1, 3, 5, 7, 9, ..., 2*N-1.
# step 3: 添加正负符号并用4除: 4/1, -4/3, 4/5, -4/7, 4/9, ...
result_pi = 0
flag = 1
for i in odd_number:
    if i % 2 ==1:
        result_pi += flag * 4/i;
        flag = -flag
# step 4: 求和:
return result_pi