Problem Statement

Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive). Show that

A (

x

1

, … ,

x

n

) ≥ G (

x

1

, … ,

x

n

) ≥ H (

x

1

, … ,

x

n

)

{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}

for this set of positive integers.

Let's start with the solution: