Let $A_{1}, G_{1}, H_{1}$ denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For $n > 2,$ let $A_{n - 1}, G_{n - 1}$ and $H_{n - 1}$ has arithmetic, geometric and harmonic means as $A_{n}, G_{N}, H_{N},$ respectively.

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Let

A_{1}, G_{1}, H_{1}

denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For

n > 2,

let

A_{n - 1}, G_{n - 1}

and

H_{n - 1}

has arithmetic, geometric and harmonic means as

A_{n}, G_{N}, H_{N},

respectively.

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Question Text

Let

A_{1}, G_{1}, H_{1}

denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For

n > 2,

let

A_{n - 1}, G_{n - 1}

and

H_{n - 1}

has arithmetic, geometric and harmonic means as

A_{n}, G_{N}, H_{N},

respectively.

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