Calculation: (((1/2))/(1+(1/2)))+(((1/3))/((1+(1/2))(1+(1/3)) ))+(((1/4))/((1+(1/2))(1+(1/3))(1+(1/4))))+…+(((1/2) 2005))/((1+(1/2))(1+(1/3))(1+(1/4))...(1+(1/2005)))).
计算：(((1/2))/(1+(1/2)))+(((1/3))/((1+(1/2))(1+(1/3))))+(((1/4))/((1+(1/2))(1+(1/3))(1+(1/4))))+…+(((1/2005))/((1+(1/2))(1+(1/3))(1+(1/4))…(1+(1/2005))))．
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">1 / 2_006</gadget>
<output>1/2_006 = around 0.000499</output>

<gadget id="calculator">(1/2) - (1/2_006)</gadget>
<output>501/1_003 = around 0.499501</output>

<gadget id="calculator">2 * (501/1_003)</gadget>
<output>1_002/1_003 = around 0.999003</output>

<result>1_002/1_003 = around 0.999003</result>