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alternating series test
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(Theorem)
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The alternating series test, or the Leibniz's Theorem, states the following:
Theorem [1,2] Let
 be a non-negative, non-increasing sequence or real numbers such that
 . Then the infinite series
 converges.
This test provides a necessary and sufficient condition for the convergence of an alternating series, since if
 converges then  .
Example: The series
 does not converge, but the alternating series
 converges to  .
- 1
- W. Rudin, Principles of Mathematical Analysis, McGraw-Hill Inc., 1976.
- 2
- E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 1993, 7th ed.
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"alternating series test" is owned by Koro. [ full author list (5) | owner history (2) ]
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Cross-references: necessary and sufficient, converges, series, infinite, real numbers, sequence
There are 6 references to this entry.
This is version 14 of alternating series test, born on 2002-02-24, modified 2008-05-11.
Object id is 2588, canonical name is AlternatingSeriesTest.
Accessed 13805 times total.
Classification:
| AMS MSC: | 40-00 (Sequences, series, summability :: General reference works ) | | | 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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