原式
=1/2x3+1/3x4+1/4x5+……+1/2005x2006
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2005-1/2006
=1/2-1/2006
=1003/2006-1/2006
=1002/2006
=501/1003