For the sequence $Z_n= ncos(n\pi/4)$. I know $S={-inf, 0, inf}$. I know this sequence has no limit, but can I say $Z_n$ is bounded? Or it is divergent to $-inf$ or $inf$?
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$Z_n$ is not bounded. Look at what happens when $n=4k$, where $k \in \mathbb{Z}$. – Anurag A Feb 16 '16 at 07:37
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It is also not divergent to $-inf$ and $inf$, correct? – J.doe Feb 16 '16 at 07:43
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What does $S$ mean? – choco_addicted Feb 16 '16 at 07:47
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It means subsequential limits of $(S_n)$ – J.doe Feb 16 '16 at 07:51
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If it has subsequences that diverge it is not bounded. – fleablood Feb 16 '16 at 08:09
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It is neither divergent to $\pm \infty$ as it has subsequence that converge. It simply does not converge and it is unbounded. – fleablood Feb 16 '16 at 08:10
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I get it! Thanks! – J.doe Feb 16 '16 at 18:43