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Topic: Alternating series question
Replies: 32   Last Post: Jun 26, 2013 10:55 PM

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Mike Terry

Posts: 655
Registered: 12/6/04
Re: Alternating series question
Posted: Apr 21, 2013 8:41 PM
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"Ray Vickson" <RGVickson@shaw.ca> wrote in message
news:9d4e47cd-e84a-4af8-88d9-74bca09ebf2e@googlegroups.com...
> Suppose we have an infinite series of the form sum{(-1)^n * a_n} where all
a_n > 0 and limit > a_n = 0 as n --> infinity. However, we do NOT assume the
a_n are monotone decreasing in n; we > just assume they --> 0. Can we still
say that the series is convergent?

1/2 - 1/1 + 1/4 - 1/2 + 1/8 - 1/3 + 1/16 - 1/4 + 1/32 - 1/5 + ...

is divergent, but meets your criteria. (I.e. interleaving the terms of a
convergent geometric series, with the terms of the divergent harmonic
series)

Mike.




Date Subject Author
4/21/13
Read Alternating series question
RGVickson@shaw.ca
4/21/13
Read Re: Alternating series question
gus gassmann
4/21/13
Read Re: Alternating series question
Mike Terry
4/21/13
Read Re: Alternating series question
gus gassmann
4/24/13
Read Re: Alternating series question
Brian Q. Hutchings
4/25/13
Read Re: Alternating series question
Robin Chapman
4/26/13
Read Re: Alternating series question
Brian Q. Hutchings
4/26/13
Read Re: Alternating series question
Robin Chapman
4/26/13
Read Re: Alternating series question
Brian Q. Hutchings
4/26/13
Read Re: Alternating series question
Brian Q. Hutchings
4/27/13
Read secondroot(secondpower(phi) plus one) -- no teragona were suffered to
find Brun's constant
Brian Q. Hutchings
6/26/13
Read Re: Alternating series question
Brian Q. Hutchings
6/26/13
Read Re: Alternating series question
Brian Q. Hutchings
4/29/13
Read secondroot(phi plus two) -- no regular tetragona were suffered to
find Brun's constant!
Brian Q. Hutchings
4/29/13
Read Big Phi: secondroot(phi plus two) -- no regular tetragona were
suffered to find Brun's constant!
Brian Q. Hutchings
4/30/13
Read Re: secondroot(phi plus two) -- no regular tetragona were suffered
to find Brun's constant!
Robin Chapman
4/30/13
Read secondroot(phi plus two) = Brun's constant phi mysticism
Brian Q. Hutchings
5/1/13
Read golden section wiitering
Robin Chapman
5/1/13
Read Re: golden section wiitering
Brian Q. Hutchings
5/2/13
Read Bullphitting
Robin Chapman
5/2/13
Read Re: Bullphitting
Brian Q. Hutchings
5/3/13
Read Re: Bullphitting
Robin Chapman
5/3/13
Read Re: Bullphitting
David C. Ullrich
5/6/13
Read Re: Bullphitting
Brian Q. Hutchings
5/7/13
Read Re: Bullphitting
Robin Chapman
5/7/13
Read Re: Bullphitting
Brian Q. Hutchings
5/9/13
Read Re: Bullphitting
Brian Q. Hutchings
5/2/13
Read Re: Alternating series question
Brian Q. Hutchings
4/23/13
Read Re: Alternating series question
RGVickson@shaw.ca
5/1/13
Read Re: Alternating series question
Brian Q. Hutchings
5/2/13
Read Re: Alternating series question
Robin Chapman

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