Also, find a subsequence such that the limit of the subsequence equals the lim sup of the sequence.
2026-04-04 19:56:07.1775332567
Construct a sequence of real numbers given the subsequential limit values. Identify the lim inf and lim sup.
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Take sequence $a_{4n+1}=1, a_{4n+2}=\sqrt{2}, a_{4n+3} = \sqrt{3}, a_{4n+4}=2$ for all $n\in \mathbb{N} \cup \{0\}$. Here $limInf(a_n) = 1 = lim(a_{4n+1})$ and $limsup(a_n) = 2 = lim(a_{4n+4})$.