∵绝对值≥0∴ab+2=0→ab=-2a+1=0→a=-1∴b=2∴1/(a-1)(b+1)+1/(a-2)(b+2)+···+1/(a-2004)(b+2004)=-(1/2*3+1/3*4+...+1/2005*2006)=-(1/2-1/3+1/3-1/4+...+1/2005-1/2006)=-(1/2-1/2006)=-501/1003