1/1X2+1/2X3+1/3X4···+1/2006X2007（怎么做呀)小弟感激不尽!

1/n(n+1)=1/n-1/(n+1)
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2006-1/2007)
=1-(1/2-1/2)-(1/3-1/3)-……-(1/2006-1/2006)-1/2007
=1-1/2007
=2006/2007

1/1*2拆成1/1-1/2
1/2*3拆成1/2-1/3
可以看见此题的规律，按上面的方法一次类推！
=1-1/2007
=2006/2007

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,

1/1*2拆成1/1-1/2
1/2*3拆成1/2-1/3
以此类推
原式=（1-1/2）+(1/2-1/3)+(1/3-1/4)+...+(1/2005-1/2006)+(1/2006-1/2007)
中间的都可以相抵消=1-1/2007
=2006/2007