基于p-级数的交错级数敛散性判别法

A New Criterion for Convergence or Divergence of Alternate Series Based on p-Series

选择p-级数作为参照级数,由比较判别法可得关于交错级数敛散性判别的一种新方法.新方法可直接判别交错级数的敛散性,并在收敛时,给出级数是条件收敛还是绝对收敛.实例说明其应用.

In this paper, a new criterion for convergence or divergence of alternate series is given based on the p-series. The new criterion can be also used to determine whether the convergent is conditionally or absolutely.