def pi(N):
    ' 计算pi的值 '
    # step 1: 创建一个奇数序列: 1, 3, 5, 7, 9, ...
    # 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, ...
    # step 4: 求和:
    s1 = itertools.count(start=1, step=2)
    s2 = list(itertools.takewhile(lambda x: x <= 2*N-1, s1))
    s3 = []
    for s in s2:
        if s % 4 == 1:
            s3.append(4/s)
        else:
            s3.append((-4)/s)
    return sum(s3)