观察下列等式： 1⼀1X2+1⼀2X3+1⼀3X4=1-1⼀2+1⼀2-1⼀3+1⼀3-1⼀4=1-1⼀4=3⼀4

观察下列等式：
1/1X2+1/2X3+1/3X4
=1-1/2+1/2-1/3+1/3-1/4
=1-1/4
=3/4
(1)直接写出下列各式的计算结果：
1/1X2+1/2X3+1/3X4+...+1/2006X2007
=1-1/2+1/2-1/3+1/3-1/4+……+1/2006-1/2007
=1-1/2007
=2006/2007

(2)探究并计算：
1/2X4+1/4X6+1/6X8+...+1/2006X2008
=1/2×（1/2-1/4+1/4-1/6+1/6-1/8+……+1/2006-1/2008）
=1/2×（1-1/2008）
=1/2×2007/2008
=2007/4016

(1)直接写出下列各式的计算结果：
1/1X2+1/2X3+1/3X4+...+1/2006X2007=1-1/2+1/2-1/3+1/3-1/4+...+1/2006-1/2007=1-1/2007=2006/2007
(2)探究并计算：
1/2X4+1/4X6+1/6X8+...+1/2006X2008
=1/4（1/1x2+1/2x3+...+1/1003x1004)=1/4*(1-1/1004)=1003/4016