作业帮(1\2+1\3)+(2\3+1\4)+(3\4+1\5)+(4\5+1\6)+.+(18\19+1\20)+(19\20+1\2)
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/14 21:08:09
(1\2+1\3)+(2\3+1\4)+(3\4+1\5)+(4\5+1\6)+.+(18\19+1\20)+(19\20+1\2)
(1\2+1\3)+(2\3+1\4)+(3\4+1\5)+(4\5+1\6)+.+(18\19+1\20)+(19\20+1\2)
(1\2+1\3)+(2\3+1\4)+(3\4+1\5)+(4\5+1\6)+.+(18\19+1\20)+(19\20+1\2)
去掉括号,得到
1/2+1/3+2/3+1/4+3/4+1/5+4/5+…+1/19+18/19+1/20+19/20+1/2
=1/2+(1/3+2/3)+(1/4+3/4)+1/5+4/5)+…+(1/19+18/19)+(1/20+19/20)+1/2
=1/2+1+1+1+…+1+1+1/2
=19
(1\2+1\3)+(2\3+1\4)+(3\4+1\5)+(4\5+1\6)+......+(18\19+1\20)+(19\20+1\2)
=1/2+(1/3+2/3)+(1/4+3/4)+(1/5+4/5)+...+(1/18+17/18)+(1/19+18/19)+(1/20+19/20)+1/2
=19