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Let A1 , G1, H1denote the arithmetic, g...

Let `A_1 , G_1, H_1`denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For `n >2,`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.

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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