对正项级数敛散性判别方法的研究

Improved Criterion for Convergence or Divergence of Positive Series Positive Series

利用函数的泰勒展开及极限的运算性质,借助已知敛散性的级数∑ 1/ n ( ln n) r 和∑ 1 /n( ln n)( ln ln n) r ,推出了判别正项级数敛散性的两个方法,并在此基础上得到了通项递减的正项级数敛散性的两个判别法.文中的结论强于双比值判别法.

In this paper, we improve two criterions for the convergence or divergence of series by comparing to ∑ 1/ n (ln n ) r and ∑ 1 /n (ln n )(lnln n ) r . We also obtain two criterions for positive series with decreasing terms. Our results are better than the double ratio criterion.