PlanetMath: Raabe's criteria

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Raabe's criteria

(Theorem)

Theorem 1 The series $a_1\!+\!a_2\!+\!a_3\!+\cdots$ with positive terms is

convergent if, starting from some value of , its terms fulfil the condition
$\displaystyle \frac{a_{n+1}}{a_n} \leqq 1-\frac{\mu}{n}$
where $\mu$ is a constant and ;
divergent if, starting from some value of , its terms fulfil the condition
$\displaystyle \frac{a_{n+1}}{a_n} \geqq 1-\frac{1}{n}-\frac{M}{n^2}$
where is a constant.

"Raabe's criteria" is owned by pahio.

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Cross-references: divergent, convergent, positive, series
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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 2226 times total.

Classification:

40-00 (Sequences, series, summability :: General reference works )

Pending Errata and Addenda

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