Observation formula: (1/(1*3))=(1/2)(1-(1/3)), (1/(3*5))=(1/2)((1/3) -(1/5)), (1/(5*7))=(1/2)((1/5)-(1/7)),…. From this calculation: (1/(1*3))+(1/(3*5))+(1/(5*7))+...+(1/(2009*2011))=how much.
观察式子：(1/(1*3))=(1/2)(1-(1/3))，(1/(3*5))=(1/2)((1/3)-(1/5))，(1/(5*7))=(1/2)((1/5)-(1/7))，…．由此计算：(1/(1*3))+(1/(3*5))+(1/(5*7))+…+(1/(2009*2011))=多少．
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">1 / 2_011</gadget>
<output>1/2_011 = around 0.000497</output>

<gadget id="calculator">1 - (1/2_011)</gadget>
<output>2_010/2_011 = around 0.999503</output>

<gadget id="calculator">(1/2) * (2_010/2_011)</gadget>
<output>1_005/2_011 = around 0.499751</output>

<result>1_005/2_011 = around 0.499751</result>