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

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 gus gassmann Posts: 60 Registered: 7/26/12
Re: Alternating series question
Posted: Apr 21, 2013 8:48 PM

On 21/04/2013 9:41 PM, Mike Terry wrote:
> "Ray Vickson" <RGVickson@shaw.ca> wrote in message

>> 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.

I stand corrected. Nice!