-1/6-1/12-1/20-1/30……-1/420

来源：百度知道编辑：UC知道时间：2024/07/05 23:35:18

1/6-1/12-1/20-1/30……-1/420
写出过程，不要只写答案

解:
-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

解：原式=-（1/6+1/12+1/20+1/30+……+1/420）
=-（1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……
+1/20-1/21）
=-（1/2-1/21）
=-19/42

5/6=1/?+1/?+1/? 1+1/3+1/6+........+1/55 1/2 ，1/3 ,1/6 /1/6 ,() (1/2) (1/4+1/6)= 1/2+1/6+1/12+1/20+1/30 1/6+1/8+1/10+1/12+..........+1/202=? 1/2+1/4+1/6+1/8+.......+1/n=? -1/2-1/6-1/12-1/20-``````````````-1/4026042 1/2+1/6+1/12+......+1/1980+1/2070=? 1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=