How to resolve the algorithm Averages/Pythagorean means step by step in the AutoHotkey programming language

Published on 12 May 2024 09:40 PM
#Autohotkey

How to resolve the algorithm Averages/Pythagorean means step by step in the AutoHotkey programming language

Table of Contents

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:

Step by Step solution about How to resolve the algorithm Averages/Pythagorean means step by step in the AutoHotkey programming language

Source code in the autohotkey programming language

A := ArithmeticMean(1, 10)
G := GeometricMean(1, 10)
H := HarmonicMean(1, 10)

If G Between %H% And %A%
    Result := "True"
Else
    Result := "False"

MsgBox, %A%`n%G%`n%H%`n%Result%


;---------------------------------------------------------------------------
ArithmeticMean(a, b) { ; of integers a through b
;---------------------------------------------------------------------------
    n := b - a + 1
    Loop, %n%
        Sum += (a + A_Index - 1)
    Return, Sum / n
}


;---------------------------------------------------------------------------
GeometricMean(a, b) { ; of integers a through b
;---------------------------------------------------------------------------
    n := b - a + 1
    Prod := 1
    Loop, %n%
        Prod *= (a + A_Index - 1)
    Return, Prod ** (1 / n)
}


;---------------------------------------------------------------------------
HarmonicMean(a, b) { ; of integers a through b
;---------------------------------------------------------------------------
    n := b - a + 1
    Loop, %n%
        Sum += 1 / (a + A_Index - 1)
    Return, n / Sum
}

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