因为1/n×1/(n+1)=1/n-1/(n+1)
则原式= -(1×1/2+1/2×1/3+.+1/2005×1/2006+1/2006×1/2007)
= -(1-1/2+1/2-1/3+.+1/2005-1/2006+1/2006-1/2007)
= -(1-1/2007)
= -2006/2007