Question

1-5/6+7/12-9/20+11/30-13/42+15/56-17/72简便方法怎么算

。。。。。帮帮我

Answer 1

Note：5/6 = （2+3）/ （ 2*3 ）= 1/2 + 1/3
1-5/6+7/12-9/20+11/30-13/42+15/56-17/72

= 1 - 1/2 - 1/3 + 1/3 + 1/4 - 1/4 - 1/5 ……+1/8
- 1/8 - 1/9

= 1 - 1/2 - 1/9

= 18/18 - 9/18 - 1/18

= 8/18

= 4/9

= 0.44444444444444444444444444444444444

Answer 2

＝1-（2+3）/(2*3)+(3+4)/(3*4)-(4+5)/(4*5)+(5+6)/(5*6)-(6+7)/(6*7)+(7+8)/(7*8)-(8+9)/(8*9)
=1-2/(2*3)-3/(2*3)+3/(3*4)+4/(3*4)-4/(4*5)-5/(4*5)+5/(5*6)+6/(5*6)-6/(6*7)-7/(6*7)+7/(7*8)+8/(7*8)-8/(8*9)-9/(8*9)
=1-1/3-1/2+1/4+1/3-1/5-1/4+1/6+1/5-1/7-1/6+1/8+1/7-1/9-1/8
=1-1/2-1/9
=7/18