Re: which values of m satisfies the inequality

*To*: mathgroup at smc.vnet.net*Subject*: [mg104231] Re: which values of m satisfies the inequality*From*: "David W. Cantrell" <DWCantrell at sigmaxi.net>*Date*: Sat, 24 Oct 2009 02:41:06 -0400 (EDT)*References*: <hbr59l$rh6$1@smc.vnet.net>

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

**Follow-Ups**:**Re: Re: which values of m satisfies the inequality***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>