Comment #3 on issue 1092 by [email protected]: 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 gives -oo in master and can probably be closed. I believe what happens is the Sum cannot be evaluated as being unbounded so it gets processed as finite in limit(); the oo is then larger and the finite term is ignored.
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