|ab-2|与|b-1|互为相反数,则ab-2=0，b-1=0b=1,a=21/(1+n)(2+n)=1/(1+n)-1/(2+n)所以1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2003)(b+2003=1-1/2+1/2-1/3+1/3-1/4……+1/2004-1/2005=1-1/2005=2004/2005
