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 fol...

$aligned & (b) A_n H_n = ab H_n = abA_n \\ & 1A_n-1 < 1A_n ( A_n < A_n-1) \\ & H_n-1 < H_n or H_1 < H_2 < H_3 < aligned$...

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?

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

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

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

. and

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

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

. and

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