May 14th, 2009, 06:39 AM  #1 
Newbie Joined: Jun 2008 Posts: 20 Thanks: 0  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? 
May 14th, 2009, 07:52 AM  #2 
Senior Member Joined: Dec 2008 Posts: 306 Thanks: 0  Re: Alternating Series converges iff converges which is which converges by the root test. Therefore the series is absolutely convergent.

May 14th, 2009, 08:22 AM  #3 
Newbie Joined: Jun 2008 Posts: 20 Thanks: 0  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 
May 14th, 2009, 02:35 PM  #4 
Senior Member Joined: Dec 2008 Posts: 306 Thanks: 0  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.

May 14th, 2009, 03:29 PM  #5 
Newbie Joined: Jun 2008 Posts: 20 Thanks: 0  Re: Alternating Series
I see. I've never seen that before... seems useful Thanks again, dman 
May 14th, 2009, 03:31 PM  #6 
Senior Member Joined: Dec 2008 Posts: 306 Thanks: 0  Re: Alternating Series
most useful with logs and fractions.


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