缺项P-级数的敛散性

The Convergence For Imperfect P-Series

P-级数(广义调和级数)+∞n=1移n1p当p>1时收敛,当0<p≤1时发散的证明方法有很多,文章通过研究缺项P-级数的敛散性,得到了一些有用的结论,并给出了P-级数敛散性的一种全新的证明.

There are many ways to prove that P-series converges when p〉 and diverges when 0〈p≤1. In this paper we consider the convergence for imperfect P-series and obtain some useful results. As a corollary of these results, we give a completely new method to prove the convergence of the P-series.