Test for Divergence: When to Use & Tips

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The discussion focuses on the confusion surrounding the Test for Divergence, particularly regarding its application to sequences and series. It clarifies that if the limit of the terms in a series does not approach zero, the series diverges. Participants emphasize the importance of distinguishing between sequences and series when applying the test. There is a call for clearer examples and definitions to resolve misunderstandings about convergence and divergence. Overall, the conversation highlights the need for precise terminology and understanding in applying the Test for Divergence effectively.
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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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