1-1/2=1/2
1/3-1=-2/3
...
1-1/2008=2007/2008
1/2009-1=-2008/2009
所以原式=(1/2)(-2/3)(3/4)(-4/5).(2007/2008)(-2008/2009)
-1共有(2009-1)/2=1004 偶数项
所以原式=1/2009