这一条怎样用简单方法算，

1/（3*4）+1/（4*5）+1/（5*6）+1/（6*7）+1/（7*8）+1/（8*9)=?
因为1/(3*4)=1/3-1/4 1/(4*5)=1/4-1/5 1/(5*6)=1/5-1/6
1/(6*7)=1/6-1/7 1/(7*8)=1/7-1/8 1/(8*9)=1/8-1/9
所以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

看见就晕了

解:原式=1/3-1/4+1/4-1/5+1/5-1/6......+1/7-1/8+1/8-1/9
=1/3-1/9=2/9

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

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)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)=2/9
这是公式:1/[(n-1)*n]=1/(n-1)-1/n(n>1)