Difficulties with limits

[ghost]

>>> print(limit_seq(Sum(1/k, (k, n, 2*n)), n))
None
>>> pprint(limit_seq(Sum(1/k, (k, n, 2*n)), n))
None

Default (Latex?) printing of limit_seq(Sum(1/k, (k, n, 2*n)), n) executes and returns nothing (I think returning nothing is better than returning the original expression)

>>> limit_seq(Sum(1/k, (k, 1, 2*n)) - Sum(1/k, (k, 1, n)), n)
log(2)

>>> a, k = symbols('a, k', positive=True, integer=True)
>>> print(limit_seq(Sum(a**k, (k, 0, n - 1)).doit()/(a**n), n))
None
>>> print(limit_seq(Sum(a**k, (k, 0, n - 1))/(a**n), n))
1/(a - 1)
>>> pprint(limit_seq(Sum(a**k, (k, 0, n - 1)).doit()/(a**n), n))
None
>>> pprint(limit_seq(Sum(a**k, (k, 0, n - 1))/(a**n), n))
  1  
─────
a - 1

Default printing of limit_seq(Sum(a**k, (k, 0, n - 1)).doit()/(a**n), n) executes and returns nothing
Default printing of limit_seq(Sum(a**k, (k, 0, n - 1))/(a**n), n) gives

  1  
─────
a - 1

a can be 1 in the above

>>> a, k = symbols('a, k', positive=True, integer=True)
>>> limit_seq(Sum(1/n, (k, 1, n)).doit()/log(n), n)
0
>>> limit_seq(Sum(1/n, (k, 1, n))/log(n), n)
1
>>> limit_seq(Sum(Rational(1,k), (k, 1, n)).doit()/log(n), n)
Traceback (most recent call last):

  File "<ipython-input-70-8de63e34fe96>", line 1, in <module>
    limit_seq(Sum(Rational(1,k), (k, 1, n)).doit()/log(n), n)

  File ".\sympy\core\numbers.py", line 1490, in __new__
    q = Rational(q)

  File ".\sympy\core\numbers.py", line 1485, in __new__
    raise TypeError('invalid input: %s' % p)

TypeError: invalid input: k

[anutosh491]

These deserve a simple heuristic which I'll be adding . The reason basically is that something like Sum(1/k, (k, a, b) ), doesn't return harmonic(b) - harmonic(a) when a is positive and returns self .

>>> print(limit_seq(Sum(1/k, (k, n, 2*n)), n))
None

Rest all faulty cases are working as expected on master as of now , (might have been fixed somewhere ) and only tests need to be added for the same

>>> limit_seq(Sum(1/n, (k, 1, n))/log(n), n)
0
>>> limit_seq(Sum(a**k, (k, 0, n - 1)).doit()/(a**n), n)
1/(a - 1)