Extension of the Bertrand-De Morgan test and its application
Abstract
We provide a simple proof for the extended Bertrand-De Morgan test that was earlier studied in [F. Duris, Infinite Series: Convergence tests. Bachelor thesis, 2009] and [A.A. Tabatabai Adnani, A. Reza and M. Morovati, J. Lin. Topol. Algebra, 2 (3), pp. 141--147 (2013)] and demonstrate an application of that test in the theory of birth-and-death processes and random walks.
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