1/1x2+1/2x3+.1/2009x2010的值
问题描述：
1/1x2+1/2x3+.1/2009x2010的值
答
1/1x2+1/2x3+.1/2009x2010=(1/1-1/2)+ (1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.+(1/2009-1/2010)=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2009-1/2010=1-1/2010(中间项全部抵消,只剩下两端的项)=2009/2010