Show that if $s_n$ and $t_n$ are two sequences in $\mathbb{R}$, then $\lim \sup (s_n + t_n) \leq \lim \sup (s_n) + \lim \sup (t_n)$
Prove $\limsup\limits_{n \to \infty} (a_n+b_n) \le \limsup\limits_{n \to \infty} a_n + \limsup\limits_{n \to \infty} b_n$