PlanetMath: ratio test

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ratio test

(Theorem)

$\displaystyle \sum_{n=1}^\infty a_n$

$\displaystyle \limsup_{n\to\infty} \left\vert\frac{a_{n+1}}{a_n}\right\vert<1$

and diverges if

$\displaystyle \liminf_{n\to\infty} \left\vert\frac{a_{n+1}}{a_n}\right\vert>1.$

"ratio test" is owned by Koro. [ full author list (2) | owner history (1) ]

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Attachments:: proof of ratio test (Proof) by vitriol
example of ratio test (Example) by drini
Raabe's criteria (Theorem) by pahio

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Cross-references: diverges, converges absolutely, series, real numbers, sequence
There are 9 references to this entry.

This is version 8 of ratio test, born on 2002-02-19, modified 2004-03-27.
Object id is 2244, canonical name is RatioTest.
Accessed 5925 times total.

Classification:

AMS MSC:	40A05 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Convergence and divergence of series and sequences)
	26A06 (Real functions :: Functions of one variable :: One-variable calculus)

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