数列与级数敛散性的关系分析

The Analysis of the Relation Between the Convergence of the Series and the Stage Number

数列与级数是两个不同的数学概念,但在敛散性关系上,有许多异同之处,这是因为二者有着密切的联系.将无穷数列的项进行连加定义了数项级数,且无穷级数的敛散性是通过其部分和数列的敛散性定义的,因此,数列和由它生成的级数,它们的敛散性有着许多联系.由敛散性的定(xn-xn-1)的敛散性是一致的,但数列{xn}与级数义,经过分析推理得到了数列{xn}与级数∑∞n=1∑∞xn的敛散性却不一致的几个结论.

The series and the stage number are two different mathematical concepts.They have some identical and different quantities in their convergent relation because they have strong link.The stage number is defined with the summation of the infinite series,while the convergence of infinite stage number is defined with the part of the stage number and the conuergence of the series.Therefore,the series and the stage number from the series have certain close relation in their convergence.