|ab-2|+（b-1)的平方=0,求 1/ab +1/（a+1)（b+1) +1/a+2）（b+2）+ .+1/（a+ 2010）（b+2010）的值

|ab-2| (b-1)的平方=0 ab-2=0,b=1 a=2,b=1 1/ab 1/(a b)(b 1) 1/(a 2)(2 b) ```````` 1/(a 2008)(b 2008) =1/1*2 1/2*3 1/3*41/2008*2009 =(1-1/2) (1/2-1/3) (1/3-1/4) . (1/2008-1/2009) =1-1/20