Two Convergence Theorems and an Extension of the Ratio Test for a Series

Zili Wu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Summary: Given a decreasing sequence (Formula presented.) of nonnegative terms, we prove that there exist subsequences (Formula presented.) of {n} such that (Formula presented.) and (Formula presented.) have the same convergence. In particular, (Formula presented.) converges if and only if (Formula presented.) converges for any natural number q > 1. Using this result, the ratio test is also extended. One example further shows that the new extended ratio test is applicable to discussing the convergence of a p-series for which the ratio test fails.

Original languageEnglish
Pages (from-to)222-227
Number of pages6
JournalMathematics Magazine
Issue number3
Publication statusPublished - 27 May 2019


  • MSC: Primary 40A05

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