1/2*5+1/5*8+1/8*11+.+1/2003*2006+1/2006*2009 =(1/2-1/5)/3+(1/5-1/8)/3+.+(1/2003-1/2006)/3+(1/2006-1/2009)/3 =(1/2-1/2009)/3 =669/4018