Word Count : 227

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To show that the set $$ S = \left\{-\frac{1}{n} + \frac{1 + (-1)^n}{3} : n \in \mathbb{N} \right\} $$ is not closed, we need to find whether it contains all its limit points. First, let's analyze the general term: $$ s_n = -\frac{1}{n} + \frac{1 _______ ________ ______ _______ _______ _________.
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