#! /usr/bin/env python
#-*-coding:utf8-*-


def shanks_once(series):
    rslt = list()

    for i in range(1, len(series)-1):
        nm1, n, np1 = series[i-1], series[i], series[i+1]
        item = (nm1*np1 - n**2) / (nm1 + np1 - 2*n)
        rslt.append(item)

    return rslt


def shanks(series, n):
    rslt = series
    for i in range(n):
        rslt = shanks_once(rslt)
    return rslt


def sum_series(series):
    rslt, item = list(), 0
    for i in series:
        item += i
        rslt.append(item)
    return rslt


if __name__ == "__main__":
    s = [
        4, -4/3, 4/5, -4/7, 4/9, -4/11, 4/13,
        -4/15, 4/17, -4/19, 4/21, -4/23, 4/25,
    ]

    s0 = sum_series(s)
    i0 = len(s0)-1
    print("%.8f" % s0[i0])

    s4 = shanks(s0, 4)
    i4 = len(s4)-1
    print("%.8f" % s4[i4])