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?

A_n-A_n-1=fracA_n-1+H_n-12-A_n-1 =fracH_n-1-A_n-12A_3> * s.

Let A_{1},G_{1} and H_{1} denote the arithmetic, geomet... | 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