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alternating series (Definition)

An alternating series is a series of the form

$\displaystyle \sum_{i = 0}^{\infty}(-1)^ia_i$

or

$\displaystyle \sum_{i = 0}^{\infty}(-1)^{i+1}a_i$

where $ (a_n)$ is a non-negative sequence. Loosely, this is just a series where the terms “alternate” between positive and negative.

For convergence issues, see the following entry: alternating series test.



"alternating series" is owned by mathcam. [ full author list (2) | owner history (1) ]
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See Also: Leibniz's theorem, proof of Leibniz's theorem (using Dirichlet's convergence test), alternating series test

Other names:  alternating series test
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Cross-references: negative, positive, sequence, series
There are 10 references to this entry.

This is version 3 of alternating series, born on 2002-02-24, modified 2005-03-25.
Object id is 2587, canonical name is AlternatingSeries.
Accessed 5668 times total.

Classification:
AMS MSC40-00 (Sequences, series, summability :: General reference works )

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