|AB-2|+|B-1|=0
所以A=2, B=1
1/AB+1/(A+1)*(B+1)+1/(A+2)*(B+2)...1/(A+2004)*(B+2004)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)...(1/2005-1/2006)
=1+(-1/2+1/2)+(-1/3+1/3)...(-1/2005+1/2005)-1/2006
=1-1/2006
=2005/2006
1
|AB-2|+|B-1|=0
所以A=2, B=1
1/AB+1/(A+1)*(B+1)+1/(A+2)*(B+2)...1/(A+2004)*(B+2004)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)...(1/2005-1/2006)
=1+(-1/2+1/2)+(-1/3+1/3)...(-1/2005+1/2005)-1/2006
=1-1/2006
=2005/2006
1