1/1*2+1/2*3+1/3*4+1/4*5.+1/2007*2008+1/2008*2009=?
问题描述：
1/1*2+1/2*3+1/3*4+1/4*5.+1/2007*2008+1/2008*2009=?
答
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/2007-1/2008)+(1/2008-1/2009)=1-1/2009=2008/2009.