Test for Divergence: When to Use & Tips

In summary: If you're talking about the limiting value of a sequence, then the answer would be "the sequence converges to 0". If you're talking about the limit of a sum, then the answer would be "the sum diverges to infinity". Please clarify which limit you're talking about.In summary, when testing for divergence, you should look for a situation where the limit of the terms in a sequence does NOT equal 0.
  • #1
krazymofo30
3
0
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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  • #2
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
 
  • #3
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.
 
  • #4
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.
 
  • #5
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
 
  • #6
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?
 
  • #7
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?
 

Related to Test for Divergence: When to Use & Tips

1. What is the purpose of a test for divergence?

A test for divergence is used to determine if an infinite series converges or diverges. It helps to identify if the terms in the series approach a finite limit or if they continue to grow infinitely.

2. When should a test for divergence be used?

A test for divergence should be used when a series does not have a clear pattern or when the terms in the series do not approach 0 as n approaches infinity. It is also useful for determining the convergence or divergence of alternating series.

3. What is the general process for conducting a test for divergence?

The general process for conducting a test for divergence involves evaluating the limit of the sequence of terms in the series. If the limit is equal to 0, the series may converge or diverge, and further tests are needed. If the limit is not equal to 0, the series is divergent.

4. Are there any tips for conducting a test for divergence?

One tip for conducting a test for divergence is to try to simplify the series before evaluating the limit. This can make it easier to determine the convergence or divergence of the series. It is also important to carefully follow the steps for each specific test for divergence.

5. Can a series be both convergent and divergent?

No, a series cannot be both convergent and divergent. It can only be one or the other. If a series passes the test for divergence and is determined to be divergent, it cannot also be convergent. However, if a series does not pass the test for divergence, it may still be convergent or divergent, and further tests are needed to determine its convergence or divergence.

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