一类幂数列的单调性

Monotony of a kind of power sequence

关于一类幂数列的单调性已经有了一些特殊结果 ,而该文以导数为工具 ,通过对幂指型函数图象特征的讨论 ,构造出一个特殊的数列 { bk} ,解决了该类幂数列的单调性 ,得到了 2个有趣的结果。当 l <b1 时 ( b1 值约 0 .40 94) ,数列是单调减少的 ,且 b1 是最大的 ;当 b1 <l <0 .5时 ,数列先单调减少到某一项 ,然后从此项开始单调增加。

In this paper,the characteristic curve of the power function with variable base and exponent is analyzed with the derivative tool, and a special sequence {b n} is formed. The monotony of the sequence is investigated,and two interesting results are obtained. When l is less than b 1 (the value of b 1is about 0.409 4), the sequence decreases monotonously and b 1 is the maximum. While the value of l ranges between b 1 and 0.5, the sequence decreases monotonously till certain term and from then on, the sequence increases monotonously.