Question

1加1/2减5/6加7/12减9/20加11/30减13/42加15/56减17/72。等于多少？

1加1/2减5/6加7/12减9/20加11/30减13/42加15/56减17/72。等于多少？请找出规律。肯定会给好评！

Answer 1

5/6=1/2+1/3,7/12=1/3+1/4,
同理可得后面的9/20,11/30,13/42,15/56,17/72.
所以原式=1+1/2-(1/2+1/3)+1/3+1/4……-(1/6+1/7)+1/7+1/8-(1/8+1/9)
=1-1/9=8/9

追问

亲，都打出来吧！

会采纳的哦

追答

9/20=1/4+1/5
11/30,=1/5+1/6

13/42=1/6+1/7
,15/56,=1/7+1/8
17/72.=1/8+1/9