1/2 + 1/2×3 ＋1/3×4 ＋……＋1/2005×2006
=1/2+1/2-1/3+1/3-1/4+＋……＋1/2005-1/2006
=1/2+1/2-1/2006
=1-1/2006
=2005/2006