View source for Du Bois-Reymond criterion (convergence of series)

{{MSC|40A05}}
{{TEX|done}}

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.

====References====
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|valign="top"|{{Ref|Kn}}|| K. Knopp,   "Theorie und    Anwendung der unendlichen Reihen" , Springer  (1964)  (English    translation: Blackie, 1951 &amp; Dover, reprint, 1990)
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