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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); –  laovultai Oct 16 '12 at 11:45
    
So you see that the "limit" does not use the "assume". –  GEdgar Oct 16 '12 at 12:35

1 Answer 1

up vote 3 down vote accepted

Well, the result -1/2-1/2*I..1/2+1.2*I means the real part of the function has all its limit points in the interval -1/2..1/2 and the imaginary part has all its limit points in the interval -1/2*I..1/2I. Of course when N is fractional, this function has non-real values. The set of limit points of this function is a circle in the complex plane, but Maple only shows a rectangle that contains it.

enter image description here

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