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#1 2014-02-18 04:10:43
- ffd
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Convergence test of series
How can we find out if the series
converges or diverges?
I tried using the root test but it was inconclusive. Please help
#2 2014-02-18 04:35:05
Re: Convergence test of series
Does not converge
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#3 2014-02-18 05:07:56
- anonimnystefy
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- From: Harlan's World
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Re: Convergence test of series
Hi ffd
Agnishom is correct. You can prove it easily by using the Limit comparison test.
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#4 2014-02-18 06:15:36
- ffd
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Re: Convergence test of series
Hi ffd
Agnishom is correct. You can prove it easily by using the Limit comparison test.
Use it how? What do you compare it with?
#5 2014-02-18 08:40:20
- anonimnystefy
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Re: Convergence test of series
Oh, yeah, forgot to say that. Compare it to 1/n.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#6 2014-02-20 02:11:46
- ffd
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Re: Convergence test of series
Oh, yeah, forgot to say that. Compare it to 1/n.
That doesn't make sense.
is a BIGGER number than . In order to compare it with another series that diverges, we must compare it with a series that is SMALLER. How did you figure?#7 2014-02-20 02:12:54
- anonimnystefy
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Re: Convergence test of series
Hi ffd
Did you look at the link I provided?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#8 2014-02-20 02:19:19
- ffd
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Re: Convergence test of series
Yes anonimnystefy I know the limit coparison test, but it seems you are using it wrong.
For a series that DIVERGES, series that are BIGGER than this series will also diverge.
BUT comparision with a SMALLER series is inconclusive. It may diverge or it may converge, we can't know for sure.
Do you see the difference?
#9 2014-02-20 02:23:49
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Convergence test of series
So far I can find no series to compare this one to. Also, other tests have been inconclusive.
Where does the problem come from?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2014-02-20 02:31:32
- ffd
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Re: Convergence test of series
Sorry anonimnystefy, I realized I mixed up the limit comparison test with the direct comparison test.
However, with the limit comparison test, I get that the limit of ak/bk is "1/(infinity^0)". As far as I know that doesn't really say anything either. Please explain how you get a conclusive answer from using this test.
#11 2014-02-20 02:32:36
- anonimnystefy
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- From: Harlan's World
- Registered: 2011-05-23
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Re: Convergence test of series
Nowhere in the statement of the test do I see a condition of the other sequence being smaller... Are you sure you actually opened the link?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#12 2014-02-20 02:36:11
- bobbym
- bumpkin
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- Registered: 2009-04-12
- Posts: 109,606
Re: Convergence test of series
I think they have phrased it poorly on that Wiki page.
If a series is term by term larger than an already known divergent series then it too is divergent. If it is smaller term by term than an already known convergent series then it too is convergent.
To prove divergence you would have to show that each term of his series is larger than each term of the Harmonic series.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#13 2014-02-20 02:37:12
- anonimnystefy
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- From: Harlan's World
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Re: Convergence test of series
Hi bobbym
You are thinking of the wrong test.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#14 2014-02-20 02:43:44
- ffd
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Re: Convergence test of series
anonimnystefy please see my last post
#15 2014-02-20 02:47:30
- anonimnystefy
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- From: Harlan's World
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Re: Convergence test of series
Hi ffd
Yes, I've seen it. I'm trying to find 1/k^(1/k) when k tends to infinity.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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