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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>