|1/11-1/10|+|1/12-1/11|+……+|1/100-1/99|

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/19 19:24:53
|1/11-1/10|+|1/12-1/11|+……+|1/100-1/99||1/11-1/10|+|1/12-1/11|+……+|1/100-1/99||1/11-1/10|+|1/12-1/11

|1/11-1/10|+|1/12-1/11|+……+|1/100-1/99|
|1/11-1/10|+|1/12-1/11|+……+|1/100-1/99|

|1/11-1/10|+|1/12-1/11|+……+|1/100-1/99|
=1/10-1/11+1/11-1/12+1/12-1/13+……+1/99-1/100
=1/10-1/100
=9/100
说明:
n>0时
n1/(n+1)
即1/n-1/(n+1)>0

|1/11-1/10|+|1/12-1/11|+……+|1/100-1/99|
=1/10-1/11+1/11-1/12+1/12-1/13+.....+1/99-1/100
=1/10-1/100 内部抵消
=9/100