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

问题描述:

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=
(2)探究并计算:
1/2X4+1/4X6+1/6X8+...+1/2006X2008

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...