这道计算题怎么做？要有方法的，追加20分。

来源：百度知道 编辑：UC知道 时间：2024/09/21 09:03:48
|1/3-1/2|+ |1/4-1/3|+ |1/5-1/4|+ …|1/10-1/9|=

不能硬算，要有方法的，，可是20分啊~~

|1/3-1/2|=1/2-1/3
|1/4-1/3|=1/3-1/4
|1/5-1/4|=1/4-1/5
......
|1/10-1/9|=1/9-1/10
所以，
原式=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/9-1/10)
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10
=1/2-1/10
=2/5

1/3-1/2<0,所以|1/3-1/2|=-(1/3-1/2)=1/2-1/3
同理
1/4<1/3,|1/4-1/3|=1/3-1/4
……
|1/10-1/9|=1/9-1/10
所以原式=1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10
中间正负抵消
=1/2-1/10
=3/10

|1/3-1/2|+ |1/4-1/3|+ |1/5-1/4|+ …|1/10-1/9|=
1/2+(-1/3+1/3)+(-1/4+1/4).....1/10
1/2-1/10=4/10

|1/3-1/2|+ |1/4-1/3|+ |1/5-1/4|+ …|1/10-1/9|
=-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-…-(1/9-1/10)
=-1/2+1/3-1/3+1/4-1/4+1/5-…-1/9+1/10（中间抵消）
=1/10-1/2
=1/10-5/10
=-4/10

|1/3-1/2|+ |1/4-1/3|+ |1/5-1/4|+ …|1/10-1/9|=1/2-1/3+1/3-……+1/9-1/10
=1/2-1/10
=2/5

绝对值里都小于0，去掉后加负号
1/2-1/3+1/3-1/4……1/9-1/10=2/5