1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/61/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6简单的计算起来

1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/61/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6简单的计算起来
1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6
1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6简单的计算起来

1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/61/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6简单的计算起来
1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1/2-1/6
=1/3

=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)=1/2-1/6=1/3

1/6+1/12+1/20+1/30=1/4+1/20+1/30=3/1

首先知道一个式子:1/n*(n+1)=1/n-1/(n+1);
所以:原式等价于 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6=1/2-1/6=1/3.

1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1/2-1/6
=1/3 这样算很简单 。。。。。。。。。。。。

1/2×1/3+1/3×1/4+1/4×1/5+1/5×1/6
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1/2-1/6
=3/6-1/6
=2/6
=1/3