发散p级数部分和公式的新证明及应用  

New proof and application of partial sum formula of divergent p series

作　　者：李苗苗 王敏 付芳芳 LI Miaomiao;WANG Min;FU Fangfang(Department of Foundation,Army Academy of Artillery and Air Defence,Hefei 230031,China)

机构地区：[1]陆军炮兵防空兵学院基础部,安徽合肥230031

出　　处：《高师理科学刊》2023年第4期11-13,共3页Journal of Science of Teachers＇College and University

摘　　要：关于发散的p级数,欧拉给出了其中调和级数的部分和公式.事实上,发散p级数在0<p<1情形下也有类似的部分和公式,给出了该部分和公式简洁证明,介绍了发散p级数部分和公式的应用.About divergent p series,Euler gave the partial sum formula of harmonic series which is one of the divergent p series.In fact,there is similar partial sum formula about divergent p series in the case of 0<p<1.A concise proof is provided for the partial sum formula,the application of the partial sum formula of the divergent p series is introduced.

关 键 词：调和级数 P级数 部分和 发散 

分 类 号：O173[理学—数学]