奥数题：1⼀2*4+1⼀4*6+1⼀6*8...+1⼀2009*2010

是不是把2008敲成2009了，按2008计算
1/2*4+1/4*6+1/6*8...+1/2008*2010
=1/2(1/2-1/4)+1/2(1/4-1/6)+1/2(1/6-1/8)+...+1/2(1/2008-1/2010)
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2008-1/2010)
=1/2(1/2-1/2010)
=1/2(505-1)/2010
=252/2010
=42/335

1/2*4+1/4*6+1/6*8...+1/2008*2010
=1/2(1/2-1/4)+1/2(1/4-1/6)+1/2(1/6-1/8)+...+1/2(1/2008-1/2010)
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2008-1/2010)
=1/2(1/2-1/2010)
=1/2（1004/2010）
=502/2010
=251/1005

最后一项应该是1/2008×2010吧。解答如下
原式＝1/2（1/2-1/4 1/4-1/6 …… 1/2008-1/2010）＝1/2（1/2-1/2010）＝251/1005
如果最后一项是1/2009×1/2010，稍微修改一下就可以了