关于对p级数敛散性研究的注记

A Note on the Research of the p-series' Convergence and Divergence

对于p级数收敛性,一般教材只给出了其随参数p的收敛性和发散性.本文归纳总结了p级数中当参数p取1,2,3时的特殊情况下的研究历史及一般情况下的推广.

When teaching the convergence and divergence of the p-series,many mathematical analysis textbooks only provide the convergence and divergence with the parameter p.This paper summarizes the research history and the main conclusion when p is1,2and3and their generalizations.