Prove that $\limsup s_n + \liminf t_n \leq \limsup (s_n + t_n)$
Properties of $\liminf$ and $\limsup$ of sum of sequences: $\limsup s_n + \liminf t_n \leq \limsup (s_n + t_n) \leq \limsup s_n + \limsup t_n$