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QJEEAdv07Ma255b: JEE Advanced 2007 Mathematics - Class 11 JEEAdv07Ma255b Solution: Let , , denote the arithmetic, geometric and harmonic means,…

Let A1{A_1} , G1{G_1} , H1{H_1} denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For n≥2, Let An−1  and  Hn−1n \ge 2,\,Let\,{A_{n - 1}}\,\,and\,\,{H_{n - 1}} have arithmetic, geometric and harminic means as An,Gn ,Hn{A_n},{G_n}\,,{H_n} repectively.

Which one of the following statements is correct ?

Multiple Choice Options

  • A H1>H2 >H3>...{H_1} > {H_2}\, > {H_3} > ...
  • B H1<H2 <H3<...{H_1} < {H_2}\, < {H_3} < ...
  • C H1>H2 >H3>...{H_1} > {H_2}\, > {H_3} > ... and H1<H2 <H3<...{H_1} < {H_2}\, < {H_3} < ...
  • D H1<H2 <H3<...{H_1} < {H_2}\, < {H_3} < ... and H1>H2 >H3>...{H_1} > {H_2}\, > {H_3} > ...

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