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Classification of the Necessary Tests of Convergence in the Theory of Numerical Series
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UDC: 514.116
Publication Language: English
Stuc. intelekt. 2013; 18(3):294-299
Abstract: The paper suggests three types of the necessary tests for the convergence of numerical series with positive terms. It is shown that these tests are consequences of the limit test of comparison with respect to the standard series: harmonic and logarithmic ones. The new tests have different capabilities and can be applied to almost any series, whose terms form a monotone sequence. The obtained necessary tests for the convergence of numerical series have more opportunities, than the accepted standard one.
Keywords: limit, L’Hospital’s rule, series, convergence, divergence, test of comparison of series, harmonic series, logarithmic series and geometric progression series.
References:
- Kudryavtsev L.D. Маtematichesky analiz. Том I., Nаukа,1970 - 571 p.
- Yevgrafov M.A. Ryady i integralniye predstavleniya –Sovremennye problem matematiki. Fundamentalniye napravleniya, T.13, 1986. 260 p.
- Ilyin V.А., Pozdniak E.G. Оsсnowy mаtematicheskogo analiza, tом 1, Izd. FML, Моskva, 1956. – 472 p.
- Fihtengolts G.М. Кurs differentsialnogo i integralnogo ischislenia, tом 2, Nauka, «FML», 1972 - 795 p.
- Apostol T.M. Calculus. One-Variable Calculus with an Introduction to Linear Algebra. Vol 1. – John Wilay and Sons, Inc., 1966, 667 with.
- Wrede R., Spiegel M. Theory and Problems of Advanced Calcolus. – Schaum’s Series, The MacGraw- Hill Companies Inc. 2002 (First Edition 1966), 433.