Let $\{a_n\}$, $\{b_n\}$ be sequences bounded above. prove $\limsup (a_n + b_n)\le \limsup(a_n) +\limsup(b_n)$
Prove $\limsup\limits_{n \to \infty} (a_n+b_n) \le \limsup\limits_{n \to \infty} a_n + \limsup\limits_{n \to \infty} b_n$