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Let A(1), G(1), H(1) denote the arithmet...

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)` has arithmetic, geometric and harmonic means as `A_(n), G_(n), H_(n)`, respectively.
Which of the following statement 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) gt H_(3) gt H_(5) gt ...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
As above `A_(1) gt H_(2) gt H_(1), A_(2) gt H_(3) gt H_(2)`
`:. H_(1) lt H_(2) lt H_(3) lt`...
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