1/8+1/24+1/48+……+1/(2012×2014)=(1/4)×[1/2+1/6+1/12+……+(1006×1007)]=(1/4)×(1-1/2+1/2-1/3+1/3-1/4+……+1/1006-1/1007)=(1/4)×(1-1/1007)=(1/4)×(1006/1007)=503/2014
