一类广义P级数的敛散性

Convergence and Divergence of a Class of Generalized P-series

从一类广义P级数的特征出发,通过分析该级数通项与项数之间的关系,重新组合该数项级数,形成一个新的交错级数.再分析原级数与新交错级数之间的关系,利用莱布尼兹判别法、柯西准则以及微分中值定理,最后给出了该级数的敛散性.

Based on the characteristics of a class of generalized P-series,this paper analyzes the relationship between its general terms and the number of terms,and recombines them to form a new interleaved series.Then,the relationship between the original and the new interleaved series is analyzed,and the convergence and divergence of the series are given by using Leibniz Test,Cauchy Criterion and Differential Mean Value Theorem.