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:

ns:=T(1,2,3,4,5,6,7,8,9,10);
ns.sum(0.0)/ns.len();					   // Arithmetic mean
ns.reduce('*,1.0).pow(1.0/ns.len());			   // Geometric mean
ns.len().toFloat() / ns.reduce(fcn(p,n){ p + 1.0/n },0.0); // Harmonic mean