Du Bois-Reymond criterion (convergence of series)

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2020 Mathematics Subject Classification: Primary: 40A05 [MSN][ZBL]

A criterion for the convergence of series of complex numbers, established by P. du Bois-Reymond.

If the series of complex numbers $\sum_n b_n$ converges and the series of complex numbers $\sum_n (a_n-a_{n+1})$ converges absolutely, then the series $\sum_n a_n b_n$ converges.


[Kn] K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990)
How to Cite This Entry:
Du Bois-Reymond criterion (convergence of series). Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article