def yield_pairs(seq):
    """ For a sequence [a,b,c,d], return the pairs (a,b), (b,c), (c,d).
    (Analogous for longer sequences.)
    """

    last = None
    for i in seq:
        if last is not None:
            yield (last, i)
        last = i


def verify_order_of_convergence(label, sequence, order):
    i = 1
    print label
    for last, current in yield_pairs(sequence):
        print "|e_%d|/|e_%d|^%g = %g" % (i+1,i,order,current/last**order)
        i += 1


verify_order_of_convergence("Method 1", [4.0e-2, 9.1e-4, 4.8e-7], 2)
verify_order_of_convergence("Method 2", [3.7e-4, 1.2e-15, 1.5e-60], 3.9)
verify_order_of_convergence("Method 2", [4.3e-3, 1.8e-8, 1.4e-24], 3)