$s_n=n\tan\frac{n\pi}{3}$
How can this sequence be decomposed to the the set of subsequences so that I can find the limit sup, and limit inf?
I suppose I could just take $n$ and then $\tan\frac{n\pi}{3}$, but I'm not entirely sure.
2026-04-03 12:14:37.1775218477
How can I find the subsequential limit, limit sup, and limit inf of $s_n=n\tan\frac{n\pi}{3}$
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Hint. One may observe that $$ s_n=n\tan\frac{n\pi}{3} = \begin{cases} 0, & \text{if $n=3\pi k$} \\[2ex] n\sqrt{3}, & \text{if $n=3\pi k+1$} \\[2ex] -n\sqrt{3}, & \text{if $n=3\pi k+2$} . \end{cases} $$