|1/3+(-1/2)|+|1/4+(-1/3)|+|1/5+(-1/4)|+……+|1/2010+(-1/2009)|

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/06 03:10:28
|1/3+(-1/2)|+|1/4+(-1/3)|+|1/5+(-1/4)|+……+|1/2010+(-1/2009)|

|1/3+(-1/2)|+|1/4+(-1/3)|+|1/5+(-1/4)|+……+|1/2010+(-1/2009)|
|1/3+(-1/2)|+|1/4+(-1/3)|+|1/5+(-1/4)|+……+|1/2010+(-1/2009)|

|1/3+(-1/2)|+|1/4+(-1/3)|+|1/5+(-1/4)|+……+|1/2010+(-1/2009)|
|1/3-1/2|+|1/4-1/3|1/5-1/4|+……+|1/100-1/99|
=1/2-1/3+1/3-1/4+1/4-1/5+.+1/99-1/100
=1/2-1/100
=49/100