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If r > 1, then the series diverges. If r = 1, the root test is inconclusive, and the series may converge or diverge. The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not conversely. [1]
ChemBioChem is a peer-reviewed scientific journal covering chemical biology, synthetic biology, and bio-nanotechnology and published by Wiley-VCH on behalf of Chemistry Europe. The journal publishes communications, full papers, reviews, minireviews, highlights, concepts, book reviews, and conference reports.
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. The test is only ...
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.
Years later, Keeler claims Cleary sent her chilling messages on Facebook admitting to the sexual assault. "So I raped you,” Cleary allegedly wrote, per the affidavit.
Abel's uniform convergence test is a criterion for the uniform convergence of a series of functions or an improper integration of functions dependent on parameters. It is related to Abel's test for the convergence of an ordinary series of real numbers, and the proof relies on the same technique of summation by parts. The test is as follows.
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The Quadrantid meteor shower is one of the strongest, and quickest, meteor showers of the year. Here’s what you need to know to observe it during peak activity.