数列单调性和不等式证明中的函数思想

数列作为以正整数集为定义域的特殊函数有其特殊性．研究数列的性质,虽然有基本的思想和方法,但是对于某些特殊的数列,用数列的思想和方法研究起来很困难,有时将其转换成函数来研究,反而比直接研究数列要简单得多．对于某些与数列有关的单调性和不等式,若将其转换成函数的单调性来研究,常常可以达到事半功倍的效果．

The Function Thought of Sequence of Monotonicity and Inequality Proof

Sequence ,as positive integer sets special function of domain ,has its particularity.For researching the nature of the sequence, there are the basic ideas and methods for studying the nature of the sequence. But for some special sequence it is difficult to study with thoughts and methods of sequence. Sometimes it is more simple to study through converting them to function rather than study sequence itself. For some monotonicity and inequality related to the sequence, if converted to monotonicity of function for studying, it often can achieve twice the result with half the effort.