Difference: ConvergenceTests (1 vs. 2)

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 META TOPICPARENT name="InfiniteSeriesSynopsis"

Convergence Tests

Table of Contents
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Name
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Statement Comments
Comparison Test Let be series with positive terms such that:

if converges then converges.
Similarly, if diverges, then diverges.
While this test is the foundation of most other tests, use it as a last resort. Other tests are often easier to apply.
Divergence Test If then may or may not converge.
Hint: Use the behavior of the limit, how goes to zero, as a clue!
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Divergence Test

Statement
Comment
then may or may not converge.
Hint: Use the behavior of the limit, how goes to zero, as a clue!

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Comparison Test

Statement
be series with positive terms such that:

converges then converges.
Similarly, diverges, then diverges.
Comment
While this test is the foundation of most other tests, use it as a last resort. Other tests are often easier to apply.

Added:
>
>

-- DickFurnas - 16 Nov 2008

Revision 12008-11-16 - Main.DickFurnas

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Added:
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 META TOPICPARENT name="InfiniteSeriesSynopsis"

Convergence Tests

Table of Contents

Name Statement Comments
Divergence Test If then may or may not converge.
Hint: Use the behavior of the limit, how goes to zero, as a clue!
Comparison Test Let be series with positive terms such that:

if converges then converges.
Similarly, if diverges, then diverges.
While this test is the foundation of most other tests, use it as a last resort. Other tests are often easier to apply.

-- DickFurnas - 16 Nov 2008

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