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Let A1, G1, H1 denote the arithmetic, ge...

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)` and `H_(n-1)` has arithmetic, geometric and harmonic means as `A_n, G_n, H_n` respectively.
Which of the following statements is correct?

A

`H_(1) gt H_(2) gt H_(3) gt…`

B

`H_(1) lt H_(2) lt H_(3) lt…`

C

`H_(1) = H_(2) = H_(3) = …. and H_(2) lt H_(4) lt H_(6) lt….`

D

`H_(1) lt H_(3) lt H_(5) lt….and H_(2) gt H_(4) gt H_(6) gt….`

Text Solution

Verified by Experts

The correct Answer is:
B
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