|1/2-1|+|1/3-1/2|+|1/4-1/3|+.……|1/20-1/19|请说明原理

|1/2-1|+|1/3-1/2|+|1/4-1/3|+.……|1/20-1/19|请说明原理
|1/2-1|+|1/3-1/2|+|1/4-1/3|+.……|1/20-1/19|
请说明原理

|1/2-1|+|1/3-1/2|+|1/4-1/3|+.……|1/20-1/19|请说明原理
因为每一个绝对值中的数相减都为负,所以去掉绝对值要在前面加负号,最终为
(-1/2)+1-(1/3)+(1/2)-(1/4)+(1/3).(-1/20)+(1/19)=1-(1/20)=19/20

|1/2-1|+|1/3-1/2|+|1/4-1/3|+.……|1/20-1/19|
=1-1/2+1/2-1/3+1/3-1/4+……+1/19-1/20
=1-1/20
=19/20

原式=1-1/2+1/2-1/3+……+1/19-1/20=1-1/20=19/20

|1/2-1|+|1/3-1/2|+|1/4-1/3|+……|1/20-1/19|
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+……+（1/19-1/20）
=1-1/20
=19/20

19/20

|1/2-1|+|1/3-1/2|+|1/4-1/3|+.……|1/20-1/19|
=1-1/2+1/2-1/3+1/3-1/4+.....+1/19-1/20
=1-1/20
=19/20

19/20