def approximate_alternating_series(f, num_decimal_points):
    '''
    returns the approximation of a convergent alternating series
    f = a function that would produce a convergent alternating series
    num_decimal_points = expected precision of approximation
    '''
    #get rid of (-1)**n in the numerator
    f_without_neg_one_to_the_n = f / sympify((-1)**n)
    #sub in n+1 for all n in the function
    f_of_n_plus_one = f_without_neg_one_to_the_n.subs(n, n+1)
    precision = 1
    for _ in range(num_decimal_points):
        precision = precision / 10
    terms = 0
    check_num_terms = f_of_n_plus_one.subs(n, terms)
    while check_num_terms > precision:
        terms = terms + 1
        check_num_terms = f_of_n_plus_one.subs(n, terms)
    approximation = 0
    for term in range(terms):
        approximation = approximation + f.subs(n, term)
    return approximation.evalf()