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Root Test
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Geliefert zwischen Mi., 28.01.2026 und Do., 29.01.2026
Details
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series. It depends on the quantity limsup{nrightarrowinfty}sqrt[n]{ an }, where an are the terms of the series, and states thats the series converges absolutely if this quantity is less than 1 but diverges if it is greater than 1. It is particularly useful in connection with power series. The terms of this series would then be given by an = cn(z p)n. One then applies the root test to the an as above. Note that sometimes a series like this is called a power series "around p", because the radius of convergence is the radius R of the largest interval or disc centred at p such that the series will converge for all points z strictly in the interior (convergence on the boundary of the interval or disc generally has to be checked separately). A corollary of the root test applied to such a power series is that the radius of convergence is exactly 1/limsup{n rightarrow infty}{sqrt[n]{ cn }}, taking care that we really mean if the denominator is 0.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131260919
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131260919
- Format Fachbuch
- Titel Root Test
- Herausgeber Betascript Publishing
- Anzahl Seiten 120
- Genre Mathematik
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