題組內容

(6) Let $\{an\}$ be a real-valued sequence and let $\sigman = (a1 + \cdots + an)/n$.



(a) (15%) Prove that $\liminf{n \to \infty} an \leq \liminf{n \to \infty} \sigman \leq \limsup{n \to \infty} \sigman \leq \limsup{n \to \infty} an$.