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

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