Test for Divergence: When to Use & Tips

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Homework Help Overview

The discussion revolves around the Test for Divergence, particularly its application in determining the convergence or divergence of sequences and series. Participants express confusion regarding the conditions under which the test should be applied and the implications of its results.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the appropriate context for using the Test for Divergence, seeking clarity on whether it applies to sequences or series. There are inquiries about the conditions that lead to divergence and how to interpret conflicting results from different problems.

Discussion Status

The discussion is ongoing, with participants providing clarifications and seeking further details. Some have suggested that the original poster clarify their statements and provide examples to facilitate understanding. There is a mix of interpretations regarding the test and its application.

Contextual Notes

There appears to be confusion regarding terminology and definitions, particularly around the concept of divergence and the specific test being referenced. Participants are encouraged to refer to their textbooks for precise definitions.

krazymofo30
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When do I use the Test for Divergence. I am confused because on some problems I get that the limit of the equation is not equal to 0 and it is convergent. But using the Test for Divergence every answer I had in the other problems would be contrary to the answer I got which I know to be right. I am just wondering when I should use the test for divergence vs. anything else. Thanks
 
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What are you testing for divergence? It sounds like you're testing an infinite sum... if the limit of the terms your summing, not the whole sum, but each individual part, doesn't go to zero, then the sum doesn't converge
 
Please clarify this. You don't say whether you are talking about divergence of sequences or series. Also there are many ways of testing for convergence- which are also then test of divergence.

I suspect that you mean "If the sequence of terms in a series does NOT converge to 0, then the series diverges". But if that's true your statement "on some problems I get that the limit of the equation is not equal to 0 and it is convergent" makes no sense. What "equation" are you talking about? And what does the "it" in "it is convergent" refer to? If you "get that the limit" of the terms is not 0, that would tell you that the series diverges, not converges.

And in "But using the Test for Divergence every answer I had in the other problems would be contrary to the answer I got which I know to be right." How did you get the answer that you "know to be right". An example of that would be helpful.
 
What I'm asking is, when is it approipraite to use the test for divergent, and whether or not I use it on a sequence or series.
 
What test for divergence are you talking about? Get out your textbook or class notes and write down exactly what it says, because what you've written is very muddled. There's definitely a most likely candidate for what you're talking about, but it's best if you clarify first
 
Test for Divergence Theorem: if limit(a[sub n]) does not equal 0 then the limit diverges.

Do I use this only with a series and not a sequence?
 
There is no "Test for Divergence Theorem" in any textbook that says anything like that!

That was why Office_Shredder said "write down exactly what it said". WHAT limit diverges?
 

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