m项交错调和级数收敛性及推广应用

The Convergence and Application of M- terms Alternative Harmonic Series

本文给出了m项交错调和级数概念,得到了交错项an(m)的两个极限值及这类级数的收敛性,给出了这类级数和的积分式及其收敛值,并把结果推广应用到通项分母呈等差数列(公差d>0)的一类交错级数求和上,解决了更多级数求和问题.

In this paper,a definition of m-terms alternative harmonic series,the convergence prop-erty of this kind of series and two limits of its alternative terms an（m）are proposed at first,then formulas to compute the sum of such series are presented. After that,these results are also generalized to alternative series that the denominator of its alternative terms make up an arithmetic sequence （the common difference d〉0）,and this generalization allow us to deal with more kinds of summation of series.