已知a-1的绝对值+ab-2的绝对值=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2000)(b+2000)
问题描述：
已知a-1的绝对值+ab-2的绝对值=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2000)(b+2000)
答
∵|a-1|+| ab-2 |=0∴a-1=0,a=1ab-2=0,b=2∴1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2000)(b+2000)=1/(1*2)+1/(2*3)+1/(3*4)+…+1/(2001*2002)=1-1/2+1/2-1/3+1/3-1/4+…+1/2001-1/2002=1-1/2002 =2001/2002