(n+ 1)/((a+b/2)(a+(n+2)b/2))^0.5-n/((a+b/2)(a+(n+ 1)b/2))^0.5>； 1/(a+(n+ 1)b) will do.

2. Basic inequality, the arithmetic mean is greater than the geometric mean, and the geometric mean is less than the arithmetic mean, so the numerator has the maximum value and the denominator has the minimum value. In short, the score has the maximum value. Just cover it up with basic inequalities.