1/1×4+1/2×5+1/3×6+L+1/2012×2015
=1/3*[(4-1)/1×4+(5-2)/2×5+(6-3)/3×6+L+(2015-2012)/2012×2015]
=1/3*[(1-1/4)+(1/2-1/5)+(1/3-1/6)+.+(1/2012-1/2015)]
=1/3(1+1/2+1/3-1/2013-1/2014-1/2015)
=1/3*[11/6-(3*2014²-1)/(2013*2014*2015)]
=11/18-(3*2014²-1)/(3*2013*2014*2015)