(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For [itex]\mu\geq 0, s\geq 1,[/itex] prove that [itex](1+s)^{\mu}\geq 1 + s^{\mu}[/itex]

2. Relevant equations

3. The attempt at a solution

I have written a proof involving the mean value theorem and derivatives, but there must be a simpler way! I think this should be done purely algebraically. Instructor insists that [itex]\mu[/itex] is an arbitrary non-negative real number, not just a rational or an integer. So to define it we need log, etc. But I believe there is a solution that does not go into this...

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# Proof involving the mean value theorem and derivatives

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