from math import log


# Funció auxiliar

def terme_salog(n):
    """Calcula el terme n-èssim de la sèrie alternada pel logaritme

    """
    return (-1)**(n+1) * 1/n


# Funcions del problema

def termes_salog(k):
    return [terme_salog(n) for n in range(1, k+1)]


def salog(k):
    sk = 0
    for n in range(1, k+1):
        sk = sk + terme_salog(n)
    return sk


def quants_termes_salog(eps):
    k = 1
    sk = terme_salog(k)
    while abs(sk - log(2)) >= eps:
        k = k + 1
        sk = sk + terme_salog(k)
    return k