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May 14th, 2009, 06:39 AM   #1
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Alternating Series

Hey, I have a question for you guys.



It's obviously convergent due to the AST, but I can't determine whether it's conditionally so or absolutely so.

I can't use the integral test, because substituting leaves me with an extra root n in the denominator.

nth term test shows that the nth term is zero, which doesn't really help.

Any other ideas?
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May 14th, 2009, 07:52 AM   #2
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Re: Alternating Series

converges iff converges which is which converges by the root test. Therefore the series is absolutely convergent.
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May 14th, 2009, 08:22 AM   #3
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Re: Alternating Series

Hey, thanks for the reply. I must confess though, that I have no idea what you did. Could you break it down for me a little bit? Sorry
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May 14th, 2009, 02:35 PM   #4
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Re: Alternating Series

if is a deacreasing positive sequence, at least eventually, then converges and diverges with . This is sometimes called cauchy's condensation test.
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May 14th, 2009, 03:29 PM   #5
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Re: Alternating Series

I see. I've never seen that before... seems useful

Thanks again, dman
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May 14th, 2009, 03:31 PM   #6
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Re: Alternating Series

most useful with logs and fractions.
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