初中奥数求助

解：因为|ab-2|与|b-1|都是非负数，它们互为相反数，那么它们都等于0，即ab=2,b=1,这时a=2,代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2004)(b+2004)
=1/(2*1)+1/(3*2)+1/(4*3)+...+1/(2006*2005)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2005-1/2006)
=1-1/2006
=2005/2006

|ab-2|与|b-1|互为相反数,
所以|ab-2|=|b-1|=0
即a=2,b=1

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2004)(b+2004)
=1/2*1+1/3*2+1/4*3+...+1/2006*2005
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2005-1/2006)
=1-1/2+1/2-1/3+1/3-1/4+....+1/2005-1/2006
=1-1/2006
=2005/2006