The tangent equation y = X-1 at the beginning of point (1, f (1)) for the image with function f (x) = ax + BX + C (a > 0) is known (I) B, C are expressed by A; (II) if f (x) > LNX is constant on [1, ∞], find the value range of A; (III) proof: 1 + 1 / 2 + 1 / 3 +. + 1 / N ≥ ln (n + 1) + n / 2 (n + 1) (n ≥ 1)

The tangent equation y = X-1 at the beginning of point (1, f (1)) for the image with function f (x) = ax + BX + C (a > 0) is known (I) B, C are expressed by A; (II) if f (x) > LNX is constant on [1, ∞], find the value range of A; (III) proof: 1 + 1 / 2 + 1 / 3 +. + 1 / N ≥ ln (n + 1) + n / 2 (n + 1) (n ≥ 1)

(I) it should be f (x) = ax * x + BX + C (a > 0). The slope of the function is equal to the derivative of the function f "(x) = 2aX + B. at the point (1, f (1)), the slope of the function is equal to the slope of the tangent line, that is, 2A + B = 1, that is, B = 1-2a