(1-1/2-1/3-..1/2012)*(1/2+1/3+...+1/2013)-(1-1/2-...-1/2013)*(1/2+1/3+...+1/2012)
=[1-(1/2+1/3+..+1/2012)]*(1/2+1/3+...+1/2012+1/2013)-[1-(1/2+...+1/2012)-1/2013]*(1/2+1/3+...+1/2012)
令t=1/2+1/3+...+1/2012,则
原式
=(1-t)*(t+1/2013)-(1-t-1/2013)*t
=(t+1/2013-t²-t/2013)-(t-t^2-t/2013)
=t+1/2013-t²-t/2013-t+t²+t/2013
=1/2013