(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1/2009)怎么算?
问题描述：
(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1/2009)怎么算?
答
首先把负号提出来,则有
1x1/2=1-1/2
1/2x1/3=1/2-1/3
1/3x1/4=1/3-1/4
.
1/2008X1/2009=1/2008-1/2009
将以上各式相加,得原式=-（1-1/2009）=-2008/2009