Calculation: (1/(1997*1998))+(1/(1998*1999))+(1/(1999*2000))+(1/(2000*2001))+(1/(2001*2002) )+(1/(2002*2003))+(1/(2003*2004))+(1/2004).
计算：(1/(1997*1998))+(1/(1998*1999))+(1/(1999*2000))+(1/(2000*2001))+(1/(2001*2002))+(1/(2002*2003))+(1/(2003*2004))+(1/2004)．
<gadget id="calculator">1_997 * 1_998</gadget>
<output>3_990_006</output>

<gadget id="calculator">1 / 3_990_006</gadget>
<output>1/3_990_006 = around 0</output>

<gadget id="calculator">1_998 * 1_999</gadget>
<output>3_994_002</output>

<gadget id="calculator">1 / 3_994_002</gadget>
<output>1/3_994_002 = around 0</output>

<gadget id="calculator">1_999 * 2_000</gadget>
<output>3_998_000</output>

<gadget id="calculator">1 / 3_998_000</gadget>
<output>1/3_998_000 = around 0</output>

<gadget id="calculator">2_000 * 2_001</gadget>
<output>4_002_000</output>

<gadget id="calculator">1 / 4_002_000</gadget>
<output>1/4_002_000 = around 0</output>

<gadget id="calculator">2_001 * 2_002</gadget>
<output>4_006_002</output>

<gadget id="calculator">1 / 4_006_002</gadget>
<output>1/4_006_002 = around 0</output>

<gadget id="calculator">2_002 * 2_003</gadget>
<output>4_010_006</output>

<gadget id="calculator">1 / 4_010_006</gadget>
<output>1/4_010_006 = around 0</output>

<gadget id="calculator">2_003 * 2_004</gadget>
<output>4_014_012</output>

<gadget id="calculator">1 / 4_014_012</gadget>
<output>1/4_014_012 = around 0</output>

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

<gadget id="calculator">(1/3_990_006) + (1/3_994_002) + (1/3_998_000) + (1/4_002_000) + (1/4_006_002) + (1/4_010_006) + (1/4_014_012) + (1/2_004)</gadget>
<output>1/1_997 = around 0.000501</output>

<result>1/1_997 = around 0.000501</result>