Published in Scientific Papers. Series E. Land Reclamation, Earth Observation & Surveying, Environmental Engineering, Vol. XIII
Written by Cosmin-Constantin NIȚU
The second criterion of comparison for the convergence of series or improper integrals, also called the limit comparison test, is a little bit unnatural and difficult for students when it comes to finding the comparison term. In this paper we give a refinement of this criteria via equivalents, which is more natural. We say that two sequences or two functions are equivalent if their quotient tends to 1 at some point. When two sequences or two integrable functions are equivalent, then their associated series or integrals have the same nature. We also present different applications of this method for both series and improper integrals.
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