简算：1+1/3-7/12+9/20-11/30+13/42-15/56

简算：1+1/3-7/12+9/20-11/30+13/42-15/56
简算：1+1/3-7/12+9/20-11/30+13/42-15/56

简算：1+1/3-7/12+9/20-11/30+13/42-15/56
1+1/3-7/12+9/20-11/30+13/42-15/56
=1+1/3-(3+4)/12+(4+5)/20-(5+6)/30+(6+7)/42-(7+8)/56
=1+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=7/8
补充(3+4）/12=3/12+4/12=1/4+1/3 其余的都是这样算

(1+3)/(1*3)-(3+4)/(3*4)+(4+5)/(4*5)-(5+6)/(5*6)+(6+7)/(6*7)-(7+8)/(7*8)
1-1/8

=1+(1/3-11/30)+(-7/12+9/20)+(13/42-15/56)
=1+1/3(1-11/10)+1/4(-7/3+9/5)+1/14(13/3-15/4)
=1+1/3(-1/10)+1/4(-8/15)+1/14(7/12)
=1+(-1/30-2/15)+1/24
=1+(-1/6+1/24)
=1+(-1/8)
=7/8