Let `a_(1), a_(2)`...be positive real numbers in geometric progression. For n, if `A_(n), G_(n), H_(n)` are respectively the arithmetic mean, geometric mean and harmonic mean of `a_(1), a_(2),..., a_(n)`. Then, 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)`