Prove that $\limsup_{n \to \infty} x_n \cdot y_n = x \cdot\limsup_{n \to \infty} y_n$
If $\lim_{n\to \infty}a_n = a\in \mathbb{R}$ . Prove that $\limsup_{n\to \infty}a_n x_n=a\limsup_{n\to \infty}x_n$ .