test_limitseq.py 文件源码

def test_limit_seq_fail():
    # improve Summation algorithm or add ad-hoc criteria
    e = (harmonic(n)**3 * Sum(1/harmonic(k), (k, 1, n)) /
         (n * Sum(harmonic(k)/k, (k, 1, n))))
    assert limit_seq(e, n) == 2

    # No unique dominant term
    e = (Sum(2**k * binomial(2*k, k) / k**2, (k, 1, n)) /
         (Sum(2**k/k*2, (k, 1, n)) * Sum(binomial(2*k, k), (k, 1, n))))
    assert limit_seq(e, n) == S(3) / 7

    # Simplifications of summations needs to be improved.
    e = n**3*Sum(2**k/k**2, (k, 1, n))**2 / (2**n * Sum(2**k/k, (k, 1, n)))
    assert limit_seq(e, n) == 2

    e = (harmonic(n) * Sum(2**k/k, (k, 1, n)) /
         (n * Sum(2**k*harmonic(k)/k**2, (k, 1, n))))
    assert limit_seq(e, n) == 1

    e = (Sum(2**k*factorial(k) / k**2, (k, 1, 2*n)) /
         (Sum(4**k/k**2, (k, 1, n)) * Sum(factorial(k), (k, 1, 2*n))))
    assert limit_seq(e, n) == S(3) / 16