原式=2007+1/2-(2006+1/3)+(2005+1/2)-(2004+1/3)+……+(3+1/2)-(2+1/3)+(1+1/2)-(0+1/3)
=(2007-2006)+(1/2-1/3)+(2005-2004)+(1/2-1/3)+……+(3-2)+(1/2-1/3)+(1-0)+(1/2-1/3)
=1*(2007+1)/2+1/6*(2007+1)/2
=7/6*1004
=3514/3
=1171又1/3