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There are many tests for determining the convergence or divergence of series. The test of Raabe and the test of Betrand are relatively unknown and do not appear in most classical courses of analysis. Also, the link between these tests and regular variation is seldomly made. In this paper we offer a unified approach to some of the classical tests from a point of view of regular varying sequences.
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We survey the connections between extreme-value theory and regular variation, in one and higher dimensions, from the algebraic point of view of our recent work on Popa groups.
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