-1/6-1/12-1/20-1/30……-1/4201/6-1/12-1/20-1/30……-1/420不要只写答案

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-1/6-1/12-1/20-1/30……-1/4201/6-1/12-1/20-1/30……-1/420不要只写答案
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-1/6-1/12-1/20-1/30……-1/4201/6-1/12-1/20-1/30……-1/420不要只写答案
-1/6-1/12-1/20-1/30……-1/420
1/6-1/12-1/20-1/30……-1/420
不要只写答案

-1/6-1/12-1/20-1/30……-1/4201/6-1/12-1/20-1/30……-1/420不要只写答案
-1/(2*3)-1/(3*4)-1/(4*5)-1/(5*6)-.-1/(19*20)-1/(20*21)
=-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-...-(1/19-1/20)-(1/20-1/21)
=-1/2+1/3-1/3+1/4-1/4+1/5-...-1/19+1/20-1/20+1/21
=-1+1/21
=-20/21