1/1*2+1/2*3+1/3*4+1/4*5=?1/1*2+1/2*3+1/3*4+1/4*5=?最好写得易懂一些

1/1*2+1/2*3+1/3*4+1/4*5=?1/1*2+1/2*3+1/3*4+1/4*5=?最好写得易懂一些
1/1*2+1/2*3+1/3*4+1/4*5=?
1/1*2+1/2*3+1/3*4+1/4*5=?最好写得易懂一些

1/1*2+1/2*3+1/3*4+1/4*5=?1/1*2+1/2*3+1/3*4+1/4*5=?最好写得易懂一些
原式=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5
=1-1/5
=4/5

1/1*2+1/2*3+1/3*4+1/4*5
=1-1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
然后括号打开全部约掉得
1－1/5=4/5
所以答案就是4/5

4/5