65656556

证明：令$\displaystyle\alpha  = \mathop {\inf }\limits_{n \ge 1} \left\{ {\frac{{\ln {a_n}}}{n}} \right\}$，由下极限的定义知\[\alpha  \le \mathop {\underline {\lim } }\limits_{n \to \infty } \frac{{\ln {a_n}}}{n}\]