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>