1/3*4+1/4*5+.+1/29*30=?

1/3*4+1/4*5+.+1/29*30=?

1/(3*4)=1/3-1/4
按次方法拆各项
就得
1/3-1/4+1/4-1/5+……+1/29-1/30=9/30

1/3*4+1/4*5+.....+1/29*30=?
=1/3-1/4+1/4-1/5+...+1/29-1/30
=1/3-1/30
=3/10

等于

1/3*4+1/4*5+.....+1/n *n+1