The convergence or divergence of the series formed by the minimum values of two monotonically decreasing divergent series of positive terms.

Asked Jun 22 '23 at 07:57

Active Jun 22 '23 at 08:27

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Given two sequences $\{a_n \}$ and $\{b_n \}$ that are both monotonically decreasing sequences of positive terms, and the series $\sum a_n$ and $\sum b_n$ both diverge, where $c_n=\min(a_n, b_n)$, can we determine the convergence or divergence of the series $\sum c_n$?

edited Jun 22 '23 at 08:27

Robert Shore

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asked Jun 22 '23 at 07:57

linchen

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Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be closed. To prevent that, please [edit] the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Jun 22 '23 at 07:58
Would this answer your question? (from AoPS) https://artofproblemsolving.com/community/c6h1922847p13188000 – Bruno B Jun 22 '23 at 08:33

The convergence or divergence of the series formed by the minimum values of two monotonically decreasing divergent series of positive terms.

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