Let and denote the arithmetic, geometric and harmonic means . respectively of two distinct positive numbers. For let and have . arithmetic, geometric and harmonic means as respectively. Which of the f...

= (Using A.M.-H.M. inequality) ...

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. Which of the following statements is correct?: Sequence & Series (Mathematics)

Let

A_{1},G_{1}

and

H_{1}

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

n \geq 2

let

A_{n - 1}

and

H_{n - 1}

have . arithmetic, geometric and harmonic means as

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

respectively. Which of the following statements is correct?

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

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

A_{1} > A_{3} > A_{5} > \ldots

. and

A_{2} < A_{4} < A_{6} < \ldots

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

. and

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