def series1(x,epsilon):
    # the two first terms
    term_prev = 1
    term_curr = x
    summ = 1
    n = 1
    while abs(term_prev-term_curr)>=epsilon:
        summ = summ + term_curr
        term_prev = term_curr
        n = n + 1
        term_curr = x**n
    return summ

def series2(x,epsilon):
    # the two first terms
    term_prev = x
    term_curr = -x**3/3
    summ = x
    n = 1
    while abs(term_prev-term_curr)>=epsilon:
        summ = summ + term_curr
#        print(term_curr)
        term_prev = term_curr
        n = n + 1
        term_curr = x**(2*n+1)/(2*n+1)
        term_curr = term_curr*(-1)**n
    return summ