Dedekind criterion (convergence of series)

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The series , where and are complex numbers, converges if the series converges absolutely, , and if the partial sums of the series are bounded.


The proof is based on the formula of summation by parts: Put for and . Then for one has

A related convergence criterion is the Dirichlet criterion (convergence of series).


[a1] W. Rudin, "Principles of mathematical analysis" , McGraw-Hill (1953)
How to Cite This Entry:
Dedekind 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