分数加减法数学题, 求过程 ,速度.1个小时以内

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|……|1/2004-1/2003|
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2003-1/2004
=1/2-1/2004
=1001/2004