View source for Dirichlet criterion (convergence of series)

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

A criterion for the convergence of the series $\sum_n a_n b_n$, where $a_n$ are real numbers and $b_n$ are complex numbers, established by P.G.L. Dirichlet in {{Cite|Di}}. If a sequence of real numbers $a_n$ converges monotonically to zero, and the sequence of partial sums of the series $\sum_n b_n$ is bounded (the terms of this series may also be complex), then the series $\sum_n a_n b_n$ converges. The criterion is related to [[Dedekind criterion (convergence of series)|Dedekind's criterion]].

====References====
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|valign="top"|{{Ref|Di}}|| P.G.L. Dirichlet,   ''J. de Math. (2)'' , '''7'''  (1862)  pp. 253–255
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