1/1x2+1/2x3+1/3x4+.+1/2003x2004等于多少
问题描述：
1/1x2+1/2x3+1/3x4+.+1/2003x2004等于多少
答
1/1x2=1/1 - 1/2
1/2x3=1/2 - 1/3
1/3x4=1/3 - 1/4
...
1/2003x2004=1/2003 -1/2004
所以： 1/1x2+1/2x3+1/3x4+......+1/2003x2004 = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/2003 -1/2004 =1 - 1/2004 = 2003/2004
答
1/1x2+1/2x3+1/3x4+.+1/2003x2004
=1-1/2+1/2-1/3+1/3-1/4+.+1/2003-1/2004
=1-1/2004
=2003/2004