Series[(2*x)^(7 + 1)*(x - Nest[Power[(# + x^2 - x), 1/2] &, 0, 7]), {x, Infinity, 5}]Series[(2*x)^(7 + 1)*(x - Nest[Power[(# + x^2 - x), 1/2] &, 0, 7]), {x, Infinity, 5}]

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