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Cauchy's convergence test. The Cauchy convergence test is a method used to test infinite series for convergence. It relies on bounding sums of terms in the series. This convergence criterion is named after Augustin-Louis Cauchy who published it in his textbook Cours d'Analyse 1821. [1]
Raabe–Duhamel's test. Let { an } be a sequence of positive numbers. Define. If. exists there are three possibilities: if L > 1 the series converges (this includes the case L = ∞) if L < 1 the series diverges. and if L = 1 the test is inconclusive. An alternative formulation of this test is as follows.
e. In mathematics, the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series. For a non-increasing sequence of non-negative real numbers, the series converges if and only if the "condensed" series converges. Moreover, if they converge, the sum of the condensed series is no more than ...
Calculus. In mathematics, the ratio test is a test (or "criterion") for the convergence of a series. where each term is a real or complex number and an is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test.
Test tubes are convenient containers for heating small amounts of liquids or solids with a Bunsen burner or alcohol burner. The tube is usually held by its neck with a clamp or tongs. By tilting the tube, the bottom can be heated to hundreds of degrees in the flame, while the neck remains relatively cool, possibly allowing vapours to condense ...
In mathematics, Dirichlet's test is a method of testing for the convergence of a series. It is named after its author Peter Gustav Lejeune Dirichlet , and was published posthumously in the Journal de Mathématiques Pures et Appliquées in 1862.
In mathematics, the limit comparison test (LCT) (in contrast with the related direct comparison test) is a method of testing for the convergence of an infinite series. Statement [ edit ]
Series. In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the limit. The test was used by Gottfried Leibniz and is sometimes known as Leibniz's test, Leibniz's rule, or the Leibniz criterion.
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