Let $\mathrm{A}_1, \mathrm{G}_1, \mathrm{H}_1$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $\mathrm{n} \geq 2$, let $\mathrm{A}_{n-1}$ and $\mathrm{H}_{n-1}$ has arithmetic, geometric and harmonic means as $\mathrm{A}_n, \mathrm{G}_n, \mathrm{H}_n$ respectively.
Which of the following statements is correct?
Select the correct option:
A
$\mathrm{H}_1>\mathrm{H}_2>\mathrm{H}_3>\ldots$
B
$\mathrm{H}_1<\mathrm{H}_2<\mathrm{H}_3<\ldots$
C
$\mathrm{H}_1>\mathrm{H}_3>\mathrm{H}_5>\ldots$ and $\mathrm{H}_2<\mathrm{H}_4<\mathrm{H}_6<\ldots$
D
$\mathrm{H}_1<\mathrm{H}_3<\mathrm{H}_5<\ldots$ and $\mathrm{H}_2>\mathrm{H}_4>\mathrm{H}_6>\ldots$
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