若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值

若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值
若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值
若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值

若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值
|ab-2|+|b-1|=0,
所以ab-2=0 b-1=0
a=2 b=1
1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)
=1/（1×2）+1/（2×3）+……+1/（2009×2010）
=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010

由|ab-2|+|b-1|=0可知b=1,a=2
1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+......+1/(a+2008)(b+2008)=1/(1X2)+1/(2X3)+...+1/(2009X2010)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+....+(1/2009-1/2010)=1-1/2010=2009/2010