It is known that A and B are rational numbers, and AB-2 and B-1 are opposite numbers to each other. Find one part of AB+[ A+1][ B+1]+[ A+2][ B+2]+…… +[ A+2008][ B+2008] value

It is known that A and B are rational numbers, and AB-2 and B-1 are opposite numbers to each other. Find one part of AB+[ A+1][ B+1]+[ A+2][ B+2]+…… +[ A+2008][ B+2008] value

|AB-2| and |B-1| areB-1=0A=2B=1AB/1+[ A+1][ B+1]/1+[ A+2][ B+2]/1+…… +[ A+2008][ B+2008]1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2009*2010)=1-1/2/2+1/2+1/3+1/3-1/4+...+1/2009-...

If the rational number a is 2 and b is 1, then 1+(a+1)(b+1)1+.(a+2004)(b+2004)1

(A+2004)(b+2004)
=1/1×2+1/2×3+1/3×4+…… +1/2005×2006
=1-1/2+1/2-1/3+1/3-1/4+…… +1/2005-1/2006
=1-1/2006
=2005/2006