Hi there, my first question here. Hope someone can give me some hints on it. Thanks!

Let $\displaystyle (x_{n})$ be a bounded sequence. For each $\displaystyle n \in \mathbb{N}$, let $\displaystyle y_{n}=x_{2n}$ and $\displaystyle z_{n}=x_{2n-1}$. Prove that

$\displaystyle \lim \sup {x_n} = \max (\lim \sup {y_n},\lim \sup {z_n})$