Dedekind criterion (convergence of series)
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)|
Dedekind criterion (convergence of series). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dedekind_criterion_(convergence_of_series)&oldid=18271