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 Post subject: A strong inequalityPosted: Thu, 11 Jun 2009 22:39:37 UTC
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Joined: Sun, 23 Mar 2008 10:55:47 UTC
Posts: 29
Prove that

.

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 Post subject: Re: A strong inequalityPosted: Fri, 12 Jun 2009 07:35:49 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7500
Location: NCTS/TPE, Taiwan
mathemagics wrote:
Prove that

.

Spoiler:
Rearrange, so it suffices to show 3>e-log(1-(e-1)/e^2). Then it is just a matter of using enough terms in the series expansion (e.g. taking 7 terms approximation for e and log) so the remainder term doesn't matter.

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 Post subject: Posted: Fri, 12 Jun 2009 13:20:06 UTC
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Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9961
I really want to use Bernoulli's inequality somehow...

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