6. In this project we will prove that the geometric mean of n numbers is no longer than the arithmetic mean of the numbers. (a) Find the maximum value of f (r1,r2, ...,In) = V2In given that r1, r2,..n are positive numbers and r1 + 2++n = c, where e is a constant. (b) Then deduce that if r1, r2, ..., In are positive numbers, then > "r... TrlxA

6. In this project we will prove that the geometric mean of n numbers is no longer than the arithmetic mean of the numbers. (a) Find the maximum value of f (r1,r2, ...,In) = V2In given that r1, r2,..n are positive numbers and r1 + 2++n = c, where e is a constant. (b) Then deduce that if r1, r2, ..., In are positive numbers, then > "r... TrlxA

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

6. In this project we will prove that the geometric mean of n numbers is no longer than the
arithmetic mean of the numbers.
(a) Find the maximum value of
f (r1,r2, ...,In) = V2In
given that r1, r2,..n are positive numbers and r1 + 2++n = c, where e is a
constant.
(b) Then deduce that if r1, r2, ..., In are positive numbers, then
> "r... TrlxA

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