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The proof of an equivalence of D’alembert’s and Cauchy’ tests in the theory of numerical series
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UDC: 514.116
Publication Language: English
Stuc. intelekt. 2013; 18(3):507-511
Abstract: In the paper it is shown that D’alembert’s test and Cauchy’s radical test are not independent one from another. It is proposed a transition scheme from one test to another and vice versa. The equivalence of the tests is proved for series with the monotonically decreasing terms. This fact is used to formulate a new test of the convergence for series with positive terms. The test is equivalent to Dalembert and Cauchy’s radical tests, but it has some advantages. It can be applied to any series within Cauchy-D’alembert’s theory.
Keywords: series, convergence, comparison tests, D’alembert’s test, Cauchy’s test, limit
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