Why does Maple gives limit as $-1/2-1/2I .. 1/2+1/2I$?

It inputted this(below) limit and it gives above output.

$limit(\frac{-\frac{1}{4}(-1)^{N+1}-\frac{1}{2}(-1)^{N+1}(N+1)+\frac{1}{4}}{N+1}, N = \infty)$

Is it right answer, or does output $-1/2-1/2I .. 1/2+1/2I$ mean that sequence is alternating sequence? ten first terms of sequence($N=0..10$): $1, -1/2, 2/3, -1/2, 3/5, -1/2, 4/7, -1/2, 5/9, -1/2, 6/11$

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This sequence quite obviously has no limit - the even terms are all $\frac{-1}{2}$, and the odd terms converge to $\frac{1}{2}$. I guess what maple returns are the limes inferior and limes superior, but what that $I$ does there, I do not know. Hm, maybe you should tell maple that $N$ is supposed to be an integer, though. As it stands, maple might interpret this as $N \in \mathbb{C}$, $|N| \to \infty$, which might explain the $I$s. – fgp Oct 16 '12 at 11:36
It gives same limit although I give assume(N::integer); – alvoutila Oct 16 '12 at 11:45
So you see that the "limit" does not use the "assume". – GEdgar Oct 16 '12 at 12:35