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| META TOPICPARENT |
name="InfiniteSeriesSynopsis" |
Convergence Tests
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| Name |
Statement |
Comments |
| Divergence Test |
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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. |
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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.
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| | -- DickFurnas - 16 Nov 2008 |
