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Let`A_(1),G_(1),H_(1)` denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For `nge2`, let `A_(n-1),G_(n-1)" and "H_(n-1)` has arithmetic,geometric and harmonic means as `A_(n),G_(n),H_(n)` respectively.
Which of the following statement is correct?

A

`H_(1)gtH_(2)gtH_(3)gt"......."`

B

`H_(1)ltH_(2)ltH_(3)lt"......."`

C

`H_(1)gtH_(3)gtH_(5)gt"......." " and " H_(2)ltH_(4)ltH_(6)lt"......."`

D

`H_(1)ltH_(3)ltH_(5)lt"......."" and " H_(2)gtH_(4)gtH_(6)gt"......."`

Text Solution

Verified by Experts

The correct Answer is:
B
As above`A_(1)gtH_(2)gtH_(1),A_(1)gtH_(3)gtH_(2)`
`:.H_(1)ltH_(2)ltH_(3)lt"......"`
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