常数项无穷级数判别法综述

Review on the Convergence-Divergence Tests of Series of Infinite Constand Terms

常数项无穷级数的审敛问题是伴随着无穷项数的和的问题而产生的一个问题。最初的问题可以追朔到公元前5世纪,而到了公元17、18世纪产生了真正的无穷级数理论,英国数学家Gregory J(1638～1675)给出了"收敛"和"发散"两个术语,由此引发了关于常数项无穷级数判别法的广泛而深入的研究,得到了一系列常数项无穷级数的判别法。时至今日,关于常数项无穷级数判别法的研究仍然比较活跃,特别是近十多年来,国内数学工作者从不同的角度或针对不同的类型提出了许多新的研究成果。为了呈现常数项无穷级数判别法的概貌,同时为进一步研究该问题提供些许素材,对常数项无穷级数的判别法进行了分类整理,并加以综述。

The problem of convergence-divergence of series of infinite constant terms is accompanied by the problem of the sum of infinite numbers. The initial problem can be traced to the 5th century BC ,and the true meaning of the theory of series emerges in the 17^th and 18^th century AD, the British mathematician Gregory J （ 1638 - 1675） gives the ＂convergence＂ and ＂divergence＂ two terms, this leads to study widely and deeply on the convergence-divergence test of series of infinite constant terms, and a lot of tests are presented. Today, the study on the convergence-divergence test of series of infinite constant terms is still active, especially over the last decade, the domestic workers in mathematics give many new research results from different angles or for different types. In order to show the over- all profile about the convergence-divergence test of the series of infinite constant series, and to provide some materials for further study at the same time, the convergence-divergence tests of the series of infinite constant series are organized by category and reviewed.