Question

Let A1, G1, H1 denoted the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For n ≥ 2, let An - 1 and Hn - 1 have arithmetic, geometric and harmonic means as An, Gn, Hn respectively. Which one of the following statements is correct? 1. H1 H2 > H3 > … 3. H1 > H3 > H5 > … and H2 H4 > H6 > …

Answer 1

Step-by-step explanation:

We know

A1>G1>H1

It is given that ′A2′ is the A.M of A1 & H1 and A1>H1

∴A1>A2>H1

′A3′ is the A.M of ′A2′ and H2 and A2>H2

∴A2>A3>H2

Hence, A1>A2>A3>…..