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Raabe's criteria
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(Theorem)
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Theorem 1 The series $a_1\!+\!a_2\!+\!a_3\!+\cdots$ , with positive terms is
- convergent if, starting from some value of $n$ its terms fulfil the condition $$\frac{a_{n+1}}{a_n} \leqq 1-\frac{\mu}{n}$$ where $\mu$ is a constant and $> 1$
- divergent if, starting from some value of $n$ its terms fulfil the condition $$\frac{a_{n+1}}{a_n} \geqq 1-\frac{1}{n}-\frac{M}{n^2}$$ where $M$ is a constant.
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"Raabe's criteria" is owned by pahio.
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Cross-references: divergent, convergent, positive, series
There is 1 reference to this entry.
This is version 4 of Raabe's criteria, born on 2005-03-21, modified 2006-09-27.
Object id is 6892, canonical name is RaabesCriteria.
Accessed 3155 times total.
Classification:
| AMS MSC: | 40-00 (Sequences, series, summability :: General reference works ) |
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Pending Errata and Addenda
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