(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+(1/42) (idea click: use split method: (1/2)= 1-(1/2), (1/6)=(1/2)-(1/3), (1/12)=(1/3)-(1/4)...then offset the middle term).
(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+(1/42)(思路点击：运用裂项法：(1/2)=1-(1/2)，(1/6)=(1/2)-(1/3)，(1/12)=(1/3)-(1/4)…然后抵消中间项)．
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">1 / 42</gadget>
<output>1/42 = around 0.02381</output>

<gadget id="calculator">(1/2) + (1/6) + (1/12) + (1/20) + (1/30) + (1/42)</gadget>
<output>6/7 = around 0.857143</output>

<result>6/7 = around 0.857143</result>