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determining series convergence
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(Topic)
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Consider a series
. To determine whether
converges or diverges, several tests are available. There is no precise rule indicating which type of test to use with a given series. The more obvious approaches are collected below.
The root test and the ratio test are direct applications of the comparison test to the geometric series with terms
and
, respectively.
For a paper about tests for convergence, please see this article.
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"determining series convergence" is owned by CWoo. [ full author list (3) | owner history (2) ]
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Cross-references: geometric series, convergent sequence, monotonic, convergent series, product, alternating series, limit comparison test, Raabe's criteria, integral test, ratio test, root test, comparison test, positive, terms, obvious, diverges, converges, series
There is 1 reference to this entry.
This is version 12 of determining series convergence, born on 2003-02-01, modified 2008-04-19.
Object id is 3958, canonical name is DeterminingSeriesConvergence.
Accessed 5554 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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