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65656556

证明:令

α =infn1{lnann}
<script id="MathJax-Element-1" type="math/tex; mode=display">\alpha = \mathop {\inf }\limits_{n \ge 1} \left\{ {\frac{{\ln {a_n}}}{n}} \right\}</script>

由下极限的定义知

α lim???nlnann
<script id="MathJax-Element-2" type="math/tex; mode=display">\alpha \le \mathop {\underline {\lim } }\limits_{n \to \infty } \frac{{\ln {a_n}}}{n}</script>