1又1/2-5/6+7/12-9/20+11/30-13/42+15/56 怎么简便运算
问题描述：
1又1/2-5/6+7/12-9/20+11/30-13/42+15/56 怎么简便运算
答
1+1/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90
=5/4-9/20+11/30-13/42+15/56-17/72+19/90
=5/4-(4+5)/4*5+(5+6)/5*6-(6+7)/6*7+(7+8)/7*8-(8+9)/8*9+(9+10)/9*10
=5/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10
=1+1/10
=11/10.
答
1又1/2-5/6+7/12-9/20+11/30-13/42+15/56 =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+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+1/8=1又1/8