Question

已知 1/2*3＝1/2-1/3，1/3-1/4＝1/12 计算1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9的结果。急！谢谢

Answer 1

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

Answer 2

1/3*4=1/3-1/4
1/4*5=1/4-1/5
.
.
.
1/8*9=1/8-1/9
1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9=1/3-1/4+1/4-1/5+1/5.....+1/7-1/8+1/8-1/9=1/3-1/9=2/9

Answer 3

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

其实有一个好明显的规律

1/(A*B)=(1/｜A-B｜)*(｜1/A-1/B｜)

Answer 4

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

Answer 5

2/9