merging What do you think about merging How to prove these inequalities: $\liminf(a_n + b_n) \leq \liminf(a_n) + \limsup(b_n) \leq \limsup(a_n + b_n)$ and Properties of $\liminf$ and $\limsup$ of sum of sequences: $\limsup s_n + \liminf t_n \leq \limsup (s_n + t_n) \leq \limsup s_n + \limsup t_n$

The one which was closed as duplicate has an interesting answer. Perhaps that answer would be more visible in the question which is not closed.

I have mentioned it at least in a comment:

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