Given that |ab-2| and |b-1| are opposite numbers, try to find the algebraic formula (1/(ab))+(1/((a+1)(b+1)))+(1/( (a+2)(b+2)))+...+(1/((a+2002)(b+2002)))=how much.
已知|ab-2|与|b-1|互为相反数，试求代数式(1/(ab))+(1/((a+1)(b+1)))+(1/((a+2)(b+2)))+…+(1/((a+2002)(b+2002)))=多少．
<gadget id="calculator">1 / 2_004</gadget>
<output>1/2_004 = around 0.000499</output>

<gadget id="calculator">1 - (1/2_004)</gadget>
<output>2_003/2_004 = around 0.999501</output>

<result>2_003/2_004 = around 0.999501</result>