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.Let `a_1, a_2,............` be positive real numbers in geometric progression. For each n, let `A_n G_n, H_n`, be respectively the arithmetic mean, geometric mean & harmonic mean of `a_1,a_2..........a_n`. Find an expression ,for the geometric mean of `G_1,G_2,........G_n` in terms of `A_1, A_2,........ ,A_n, H_1, H_2,........,H_n`.

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