Abstract:

We prove the characterization of the convergence of a class of series with positive terms can be conducted by the convergence of a relevant monotone positive sequence.Based on some  questions in the preliminary contest of National College Student Mathematics Competitions and some questions in the  "mathematical analysis" of the graduate entrance examination,some examples are provided to illustrate the applications of the results in solving the problems of series convergence.

Key words: series with positive terms, sequence of numbers, convergence