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Cross-references: absolutely convergent, complex, divergent, infinite, convergent, terms, real, positive, series
There are 3 references to this entry.
This is version 6 of Cauchy's root test, born on 2002-08-23, modified 2006-10-24.
Object id is 3337, canonical name is CauchysRootTest.
Accessed 6032 times total.
Classification:
| AMS MSC: | 40A05 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Convergence and divergence of series and sequences) |
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Pending Errata and Addenda
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![$\displaystyle \sqrt[n]{a_{n}} < k < 1$](http://images.planetmath.org:8080/cache/objects/3337/l2h/img2.png "$\displaystyle \sqrt[n]{a_{n}} < k < 1$"){kind=small}
![$ \sqrt[n]{a_{n}} \geq 1$](http://images.planetmath.org:8080/cache/objects/3337/l2h/img5.png "$ \sqrt[n]{a_{n}} \geq 1$"){kind=small}
![$\displaystyle \rho = \limsup_{n \to \infty} \sqrt[n]{\vert a_{n} \vert}$](http://images.planetmath.org:8080/cache/objects/3337/l2h/img9.png "$\displaystyle \rho = \limsup_{n \to \infty} \sqrt[n]{\vert a_{n} \vert}$"){kind=small}
