(1/(1+2))+(1/(1+2+3))+(1/(1+2+3+4))+…+(1/(1+2+3+…+ 2003)).
(1/(1+2))+(1/(1+2+3))+(1/(1+2+3+4))+…+(1/(1+2+3+…+2003))．
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">1 / 2_004</gadget>
<output>1/2_004 = around 0.000499</output>

<gadget id="calculator">(1/2) - (1/2_004)</gadget>
<output>1_001/2_004 = around 0.499501</output>

<gadget id="calculator">2 * (1_001/2_004)</gadget>
<output>1_001/1_002 = around 0.999002</output>

<result>1_001/1_002 = around 0.999002</result>