Comment #12 on issue 1092 by smi...@gmail.com: limit(sum(1/k, (k, 1, n))-log(n), n, oo) should do it
http://code.google.com/p/sympy/issues/detail?id=1092

This now returns

limit(summation(1/k, (k, 1, n))-log(n), n, oo)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "sympy\series\limits.py", line 216, in limit
    r = heuristics(e, z, z0, dir)
  File "sympy\series\limits.py", line 221, in heuristics
return limit(e.subs(z, 1/z), z, S.Zero, "+" if z0 is S.Infinity else "-")
  File "sympy\series\limits.py", line 216, in limit
    r = heuristics(e, z, z0, dir)
  File "sympy\series\limits.py", line 239, in heuristics
    raise PoleError(msg % (e, z, z0, dir))
sympy.core.function.PoleError: Don't know how to calculate the limit(-log(1/n) +
 harmonic(1/n), n, 0, dir=+), sorry.


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