1又2分之1-6分之5+12分之7-20分之9+30分之11-42分之13+56分之15······
1又2分之1-6分之5+12分之7-20分之9+30分之11-42分之13+56分之65-72分之17+90分之19-110分之21
(1+1/2)-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90-21/110
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)
-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)-(1/10+1/11)
=1+(1/2-1/2)+(-1/3+1/3)+(1/4-1/4)+(-1/5+1/5)+
(1/6-1/6)+(-1/7+1/7)+(18-1/8)+(-1/9+1/9)+(1/10-1/10)-1/11
=1-1/11
=10/11
解答：原式=(1+1/2)-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90-21/110
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)-(1/10+1/11)
=1+(1/2-1/2)+(-1/3+1/3)+(1/4-1/4)+(-1/5+1/5)+(1/6-1/6)+(-1/7+1/7)+(18-1/8)+(-1/9+1/9)+(1/10-1/10)-1/11
=1-1/11
=10/11。
1又1/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90-21/110
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)-(1/10+1/11)
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+
1/8-1/8-1/9+1/9+1/10-1/10-1/11
=1-1/11
=10/11
你拆一下，1又2分之1是1+1/2,5/6是1/2+1/3,7/12=1/3+1/4……
到后面化出来的就是1+1/2-1/2-1/3+1/3+1/4-1/4-1/5……+1/9+1/10-1/10-1/11=1-1/11=10/11
1又1/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90-21/110
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)-(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)-(1/10+1/11)
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10-1/10-1/11
=1-1/11
=10/11
1+1/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90-21/110
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)-(1/10+1/11)
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10-1/10-1/11
=1-1/11
=10/11
1又2分之1-6分之5+12分之7-20分之9+30分之11-42分之13+56分之65-72分之17+90分之19-110分之21
=1+2分之1-6分之5＋12分之7－20分之9＋30分之11－42分之13+56分之65-72分之17+90分之19-110分之21
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)
-(1/10+1/11)
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10-1/10-1/11
=1-1/11
=10/11