(b) Consider the degree n version of the AM/GM inequality, which states for positive real numbers x₁,x2,...,xn that x₁ + x₂ + + xn n ... >√√xx₂xn (i) Fove that if the AM/GM inequality is true for n=k, then it will be true for n = 2k. (ii) Prove that if the AM/GM inequality is true for n=k, then it will be true for n = k-1 (iii) Hence explain why the AM/GM inequality is true for all positive integers n.

(b) Consider the degree n version of the AM/GM inequality, which states for positive real numbers x₁,x2,...,xn that x₁ + x₂ + + xn n ... >√√xx₂xn (i) Fove that if the AM/GM inequality is true for n=k, then it will be true for n = 2k. (ii) Prove that if the AM/GM inequality is true for n=k, then it will be true for n = k-1 (iii) Hence explain why the AM/GM inequality is true for all positive integers n.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 80E

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