题目应是 1/6+1/12+1/20+1/30+……（省略号）+1/2005*2006
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/2005-1/2006
=1/2-1/2006
=1002/2006
=501/1003