|1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10| |1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10|
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 22:23:00
![|1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10| |1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10|](/uploads/image/z/7397899-43-9.jpg?t=%7C1%2B1%2F2%7C-%7C1%2F2%2B1%2F3%7C%2B%7C1%2F3%2B1%2F4%7C-%E2%80%A6%E2%80%A6%2B%7C1%2F9%2B1%2F10%7C+%7C1%EF%BC%8B1%2F2%7C%EF%BC%8D%7C1%2F2%2B1%2F3%7C%2B%7C1%2F3%2B1%2F4%7C%EF%BC%8D%E2%80%A6%E2%80%A6%2B%7C1%2F9%EF%BC%8B1%2F10%7C)
|1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10| |1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10|
|1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10|
|1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10|
|1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10| |1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10|
|1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10|
=(1+1/2)-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10
=1+1/10
=11/10
1加1/10
|1+1/2|-|1/2+1/3|+|1/3+1/4|-...-|1/8+1/9|+|1/9+1/10|
=(|1+1/2|+|1/3+1/4|+...+|1/9+1/10|)-(|1/2+1/3|+|1/4+1/5|+...+|1/8+1/9|)
=(1+1/2+1/3+1/4+...+1/9+1/10)-(1/2+1/3+1/4+1/5+...+1/8+1/9)
=1+...
全部展开
|1+1/2|-|1/2+1/3|+|1/3+1/4|-...-|1/8+1/9|+|1/9+1/10|
=(|1+1/2|+|1/3+1/4|+...+|1/9+1/10|)-(|1/2+1/3|+|1/4+1/5|+...+|1/8+1/9|)
=(1+1/2+1/3+1/4+...+1/9+1/10)-(1/2+1/3+1/4+1/5+...+1/8+1/9)
=1+1/10
=11/10
收起
|1+1/2|-|1/2+1/3|+|1/3+1/4|-……+|1/9+1/10|
=1+1/2-1/2-1/3+1/3+1/4-……-1/8-1/9+1/9+1/10
=1+1/10
=11/10