If the rational number a, b satisfies |ab-2|+(1-b)**2=0; try to find (1/(ab))+(1/((a+1)(b+1)))+ The value of (1/((a+2)(b+2)))+…+(1/((a+2010)(b+2010))).
如果有理数a，b满足|ab-2|+(1-b)**2=0；试求(1/(ab))+(1/((a+1)(b+1)))+(1/((a+2)(b+2)))+…+(1/((a+2010)(b+2010)))的值．
<gadget id="calculator">1 / 2_012</gadget>
<output>1/2_012 = around 0.000497</output>

<gadget id="calculator">1 - (1/2_012)</gadget>
<output>2_011/2_012 = around 0.999503</output>

<result>2_011/2_012 = around 0.999503</result>