|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|－……+|1/9＋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