|ab-2|+(b+1)^2=0
那么ab-2=0 b+1=0
得a=-2 b=-1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2007)(b+2007)
=1/2+1/1*2+1/2*3+1/3*4+.+1/2005*2006
=1/2+(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2005-1/2006)
=1/2+1-1/2006
=3008/2006
=1504/1003
|ab-2|+(b+1)^2=0
那么ab-2=0 b+1=0
得a=-2 b=-1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2007)(b+2007)
=1/2+1/1*2+1/2*3+1/3*4+.+1/2005*2006
=1/2+(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2005-1/2006)
=1/2+1-1/2006
=3008/2006
=1504/1003