作业帮|1/2004-1/2003|+|1/2002-1/2003|+.+|1/2-1|等于多少 |1/2004-1/2003
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/19 04:51:50
|1/2004-1/2003|+|1/2002-1/2003|+.+|1/2-1|等于多少 |1/2004-1/2003|+|1/2002
|1/2004-1/2003|+|1/2002-1/2003|+.+|1/2-1|
=|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2003-1/2002|+|1/2004-1/2003|
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2002-1/2003)+(1/2003-1/2004)
=1-1/2004
=2003/2004
=|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2003-1/2002|+|1/2004-1/2003|
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2002-1/2003)+(1/2003-1/2004)
=1-1/2004
=2003/2004