Question

3乘4分之1+4乘5分之1+5乘6分之1+6乘7分之1 +7乘8分之1 +8乘9分之1的结果是多少？

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
=2/9

追问

再详细地分析一下吧！！！！！！！！！！

追答

分数裂项
1/(3×4)=1/3-1/4
1/(4×5)=1/4-1/5
......
1/(8×9)=1/8-1/9
中间互相抵消,最后就剩下1/3-1/9=2/9