摘要：正项级数敛散性的判别问题，通项本身的形式很复杂，需要对级数通项进行放缩，从而达到化简，从而求解的目的，里面的技巧性很高，像这类问题在各种竞赛题及考研题中大量出现。本论文通过对这类问题的论述，给出其若干处理方法，以便于处理此类问题。先总述各种正项级数的解决方法，进而论述正项级数比较法中不等式的各种缩放法，再进一步详细论正项级数比较判别法中不等式缩放的具体步骤。

关键词：正项级数；  收敛； 发散；不等式缩放 

Abstract：The problem of how to distinguish Positive series between convergence and divergence is very complex ,especially in terms of the form of general term . The general term needs to be magnified and minified so that it will be reducible and settled, which includes high skill. Such kind of problems often occur in the contests and the post graduate examination. This dissertation will give some approaches to solving such kind of problems by analyzing all aspects of it. Firstly, I will give a general introduction to the solutions of how to solve all kinds of positive series, then I will describe the way of how to magnify and minify in all kinds of inequality . Lastly, I will describe the detailed steps of the magnify and minify of inequality in the way of how to discriminate positive series.

Keywords: Positive series ; convergence ; divergent ; Inequality zoom 

本文主要研究正项级数比较判别法中不等式缩放的应用。本论文通过对这类问题的分析，给出了具体可能出现的步骤，以便于处理该类问题。先总述正项级数的定义和各种解决方法，再进一步详细论述了正项级数比较判别法中不等式缩放的具体用法。研究怎样使用不等式缩放在正项级数比较法中的应用，重点写了不等式缩放在正项级数中比较法的巧妙利用。