1/1*4+1/4*7+1/7*10+...+1/2005*2008+1/2008*2011=1/3*(1/1-1/4)+1/3*(1/4-1/7)+...+1/3*(1/2005-1/2008)+1/3*(1/2008-1/2011)=1/3*[(1-1/4)+(1/4-1/7)+...+(1/2005-1/2008)+(1/2008-1/2011)]=1/3*(1-1/2011)=670/20...