Word Count : 99

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Let $a_n=-\frac{1}{n}+\frac{1+(-1)^n}{3}$ so that $S=\{a_n:n\in\mathbb N\}$. For odd $n=2k+1$ we have $a_{2k+1}=-\dfrac{1}{2k+1}$; for even $n=2k$ we ________ ____ ______ ______ ___ _____ ______.
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