**63. Let aj, az, ..., a, be positive real numbers. The arith-metic mean of these numbers is defined byA = (a, +a, + …· +a„,)/n,and the geometric mean of these numbers is defined byG= (a,a2 .. a„)'/".Use mathematical induction to prove that A 2 G.

The arithmetic mean AM=a1+a2+...+annThe geometric mean GM=(a1,a2...,am)1n We need to show A≥G.

Answered: * 63. Let a¡, az» ·… , A, be positive…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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* 63. Let a¡, az» ·… , A, be positive real numbers. The arith- metic mean of these numbers is defined by ... A = (a, +a, + .…· + a,)/n, ... and the geometric mean of these numbers is defined by G = (a¡az .…. a„)\/". Use mathematical induction to prove that A 2 G.