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Topic: Help with an inequality
Replies: 3   Last Post: Aug 1, 2007 12:53 PM

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Jon Haugsand

Posts: 344
Registered: 12/6/04
Re: Help with an inequality
Posted: Aug 1, 2007 12:53 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> Hey all,
> I get the following problem.
> Given:
> 1) {ai},{bi},{xi} and {yi} are postive and their corresponding
> infinite series converge.
> 2) sum{i=1,...,infinity}ai*xi=sum{i,...,infinity}bi*yi
> 3) for any n,m>=1, an<=bm
> Question:
> Does it always hold
> sum{i=1,...,infinity}xi>=sum{i=1,...,inifinity}yi?
> I really appreciarte any of your comment.

Is this possible? According to (1), each sequence must approach
zero. Therefore (3) cannot hold.

(Or am I missing something?)

Jon Haugsand
Dept. of Informatics, Univ. of Oslo, Norway,, Phone: +47 45 00 39 94

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