1/1x2+1/2x3+1/3x4+...+1/2007
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2007)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2007
中间互相抵消
=2006/2007
参考资料：仅供参考,