Prove that $\limsup_{n \to \infty} \left(a_n + b_n \right) \leq \limsup_{n \to \infty} a_n +\limsup_{n \to \infty} b_n$
Prove $\limsup\limits_{n \to \infty} (a_n+b_n) \le \limsup\limits_{n \to \infty} a_n + \limsup\limits_{n \to \infty} b_n$