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A rearrangement of the comparison tests in the theory of number series
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UDC: 514.116
Publication Language: Russian
Stuc. intelekt. 2013; 18(1):36–41
Abstract: In the paper a theorem that connects the geometrical series with the zeta-function and the logarithmic series is proposed. The theorem rearranges the standard series according to a speed of the convergence of the series. The theorem has mainly a theoretical character but it can be used for an estimation of a convergence of series with non-negative terms. The theorem is adopted to improper integrals.
Keywords: series, convergence, zeta-function, logarithmic series, comparison tests, integral test
References:
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- Cinlar E. Vanderbei R.J. Mathematical Methods of Engineering Analysis. 2000. 119 p.