∵x,y互为相反数,即x+y=0
∴x+2x+3x+.+2006x+2007x+2007y+2006y+.+3y+2y+y
=(x+y)+2(x+y)+3(x+y)+...+2006(x+y)+2007(x+y)
=0+0+0+...+0+0
=0