MHB Are the Accumulation Points of the Series $(-1)^n/[1 + (1/n)]$ Open at 1 and -1?

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All numbers of the form $(-1)^n/[1 + (1/n)]$, $n\in\mathbb{Z}^+$.

$(-1)^n/[1 + (1/n)] = (-1, 1)$ is that true?
 
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dwsmith said:
All numbers of the form $(-1)^n/[1 + (1/n)]$, $n\in\mathbb{Z}^+$.

$(-1)^n/[1 + (1/n)] = (-1, 1)$ is that true?

For what $n\in\mathbb{Z}^+$ does $-2/3=(-1)^n/[1 + (1/n)]$

CB
 
So the accumulation points are 1 and -1 and the set is open then.
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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