I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition).(adsbygoogle = window.adsbygoogle || []).push({});

I am focused on Chapter 2: Sequences and Series of Real Numbers ... ...

I need help with the proof of Proposition 2.1.25 ...

Proposition 2.1.25 reads as follows:

In the above proof, Sohrab appears to be using mathematical induction ... BUT ... he proves the inequality for ##n= 2##, but then, in the inductive step, instead of assuming the inequality is true for ##n## and then proving it is true for ##n+1## ... Sohrab assumes the inequality is true for ##n = 2^m## and then proceeds to prove it true for ##2n = 2^{ m+1}## ... then finishes the proof by picking an ##m## such that ##n \lt 2^m## and establishing the inequality ...

My questions are as follows:

What is the valid proof process here ... ?

How does the proof process fit with the usual mathematical induction strategy ...

Peter

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# I The AM-GM Inequality - Sohrab Proposition 2.1.25 ...

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