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Re: Re: which values of m satisfies the inequality

• To: mathgroup at smc.vnet.net
• Subject: [mg104276] Re: [mg104231] Re: which values of m satisfies the inequality
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 25 Oct 2009 01:10:54 -0400 (EDT)
• References: <hbr59l$rh6$1@smc.vnet.net> <200910240641.CAA07606@smc.vnet.net>

On 24 Oct 2009, at 15:41, David W. Cantrell wrote:

> barefoot gigantor <barefoot1980 at gmail.com> wrote:
>> for what value or interval of m (-infinity < m < infinity) the  
>> following
>> is valid
>>
>> (1+x)^(m+1) > (1+x^m)* 2^m
>>
>> here x >=1
>
> I shall assume that you really meant to have strictly x > 1. [That's
> because, if x = 1, then (1+x)^(m+1) = (1+x^m) * 2^m, regardless of m.]
>
> Answer:
>
> For x > 1 and m >= -1,
>
> (1+x)^(m+1) > (1+x^m) * 2^m
>
> David
>


Hmm...

(1 + x)^(m + 1) > (1 + x^m)*2^m /. {x -> 10, m -> 6}

  False

Andrzej Kozlowski

• References:
  • Re: which values of m satisfies the inequality
    • From: "David W. Cantrell" <DWCantrell@sigmaxi.net>