级数求和中的裂项法研究

Research on the Sum of Series by Crack Method

级数是表示函数、研究函数性质以及进行数值计算的有力工具,在数学和其他学科中经常会遇到级数求和的问题,利用裂项相消法和裂项后应用已知级数求和公式的方法,推出了几类级数的求和公式,利用这些求和公式求得了一些常见级数的和,得到了能求其和的几种级数类型,给出了用裂项法求级数和的方法。

Series is a powerful tool for representing functions, studying function properties and performing numerical calculations. In mathematics and other disciplines, we often encounter the problem of summation of stages. By using the method of fission cancellation and the method of calculating the summation formula of known series after the fission, the summation formula of several series is introduced. Using these summation formulas, the sum of some common series is obtained, and the sum of several series types gives the method of summation of series.