Cesàro可和级数性质探讨

The Nature of Convergence Series under Cesàro

对级数在Cesàro意义下收敛的问题进行探讨,得到级数在Cesàro意义下收敛的一些性质,如Cesàro和与级数在通常意义下收敛的和的关系,级数可Cesàro求和的必要条件,级数在通常意义下收敛与Cesàro意义下收敛的关系等,进而更完整地解决了级数在Cesàro意义下收敛性的判定方法.

In this paper, the convergence series in the sense of Cesaro were discussed, and some properties of the convergence series in the sense of Cesaro were obtained, such as the relationship between the sum of the convergence numerical series in the usual sense and the sum of the convergence numerical series in the Cesaro sense, the necessary condition of the convergence numerical series in the Cesaro sense and the relationship between the convergence of numerical series in the usual sense and the convergence of numerical series in the Cesaro sense. Thus a more complete solution to the problem of determination method for converges series in the sense of Cesaro was obtained.