快快快！
ab-2=0,1-b=0
a=2,b=1
1/ab+1/(a+1)(b+1)+……+1/首雹（a+2003)(b+2003)
=1/(2*1)+1/(3*2)+…迟芹肢…+1/(2005*2004)
=(1-1/2)+(1/2-1/码世3)+……+(1/2004-1/2005)
=1-1/2005
=2004/2005
因为有理数坦悄带a、b满足|ab-2|加（让芦1-b)的2次方=0
所以A=2，B=1~~
1/ab+1/(a+1)(b+1)+……+1/（a+2003)(b+2003)
=1/(2*1)+1/运祥(3*2)+……+1/(2005*2004)
=(1-1/2)+(1/2-1/3)+……+(1/2004-1/2005)
=1-1/2005
=2004/2005