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

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The discussion centers on the accumulation points of the series defined by the expression $(-1)^n/[1 + (1/n)]$ for positive integers n. It is established that the values oscillate between -1 and 1, leading to the conclusion that the accumulation points are indeed 1 and -1. The set of accumulation points is considered open, as it does not include the endpoints. A specific query regarding the equality $-2/3=(-1)^n/[1 + (1/n)]$ is raised, though it does not alter the main conclusion about the accumulation points. Overall, the series demonstrates an oscillatory behavior with clear accumulation points at 1 and -1.
Dustinsfl
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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.
 

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