已知,|ab-2|+（b-1）² = 0 ,因为,|ab-2| ≥ 0 ,（b-1）² ≥ 0 ,所以,|ab-2| = 0 ,（b-1）² = 0 ,可得：ab-2 = 0 ,b-1 = 0 ,解得：a = 2 ,b = 1 ；1/ab+1/( a+1)(b+1)+.+1/(a+2000)(b+2000)= 1/(1*2)+...