Názov:Infinite series: Convergence tests
Vedúci:doc. RNDr. Zbyněk Kubáček, CSc.
Kľúčové slová:Infinite series, convergence, divergence, Kummer, Gauss, Bertrand, Raabe.
Abstrakt:The theory of infinite series, an old and well examined part of calculus, gives us a powerfull tool for solving a wide range of problems such as evaluating important mathematical constants (e, pi, ...), values of trigonometric functions etc. This thesis introduces the idea of infinite series with some basic theorems necessary in the following chapters. Then building on this, it derives some convergence tests, namely Raabe's test, Gauss' test, Bertrand's test and Kummer's test. It also proves that there is no universal comparison test for all series.

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