Let A_{1},G_{1} and H_{1} denote the arithmetic, geometric and harmonic means . respectively of two distinct positive numbers. For n ? 2 let A_{n - 1} and H_{n - 1} have . arithmetic, geometric and harmonic means as A_{n},G_{n},H_{n} respectively.: Sequence & Series (Mathematics) Question | DivineJEE

Let

A_{1},G_{1}

and

H_{1}

denote the arithmetic, geometric and\nharmonic means . respectively of two distinct positive numbers. For\n

n \geq 2

let

A_{n - 1}

and

H_{n - 1}

have . arithmetic,\ngeometric and harmonic means as

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

respectively.

G_{1} > G_{2} > G_{3} > \ldots

G_{1} < G_{2} < G_{3} < \ldots

G_{1} = G_{2} = G_{3}\ldots

G_{1} < G_{3} < G_{5}\ldots

and

G_{2} > G_{4} > G_{6}\ldots

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