|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2004-1/2003|怎么算

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2004-1/2003|怎么算
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2004-1/2003|怎么算

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2004-1/2003|怎么算
分析：
because 1/2大于1/3,1/3大于1/4,.
所以 |1/3-1/2|=-（1/3-1/2）=1/2-1/3
原式=1/2-1/3+1/3-1/4+...+1/2003-1/2004
=1001/2004