# Dedekind criterion (convergence of series)

From Encyclopedia of Mathematics

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

#### Comments

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).

#### References

[a1] | W. Rudin, "Principles of mathematical analysis" , McGraw-Hill (1953) |

**How to Cite This Entry:**

Dedekind criterion (convergence of series).

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Dedekind_criterion_(convergence_of_series)&oldid=18271

This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article