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Paragraph: Let A₁, G₁, H₁ denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For n 2 , let A_ n-1 and H_ n-1 has arithmetic, geometric and harmonic means as A_n, G_n, H_n , respectively. Question: Which of the following statements is correct?

Options

  1. AH ₁> H ₂> H ₃>
  2. BH₁ < H₂ < H₃ <
  3. CH₁>H₃>H₅> and H₂ < H₄ < H₆ <
  4. DH ₁ H ₄> H ₆>

Correct answer

B. H₁ < H₂ < H₃ <

Step-by-step solution

As above A₁>H₂>H₁, A₂>H₃>H₂ H₁ < H₂ < H₃ <

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