Let $${A_1}$$, $${G_1}$$, $${H_1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \ge 2,\,Let\,{A_{n - 1}}\,\,and\,\,{H_{n - 1}}$$ have arithmetic, geometric and harminic means as $${A_n},{G_n}\,,{H_n}$$ repectively.
Which one of the following statements is correct ?
A
$${A_1} > {A_2}\, > {A_3} > ...$$
B
$${A_1} < {A_2}\, < {A_3} < ...$$
C
$${A_1} > {A_2}\, > {A_3} > ...$$ and $${A_1} < {A_2}\, < {A_3} < ...$$
D
$${A_1} < {A_2}\, < {A_3} < ...$$ and $${A_1} > {A_2}\, > {A_3} > ...$$