1×2分之1＋2×3分之1＋3×4分之1＋.＋2005×2006分之1＋2006×2007分之1
=1-1/2+1/2-1/3+1/3-1/4+.+1/2005-1/2006+1/2006-1/2007
=1-1/2007
=2006/2007