a*b=a-b/ab.例:2*(-3)=2-(-3)/2×(-3)=-5/6

1*2+2*3+3*4+...+2007*2008
=(1-2)/1*2+(2-3)/2*3+(3*4)/3*4+...+(2007-2008)/2007*2008
=-1/1*2-1/2*3-1/3*4-...-1/2007*2009
=-(1/1*2+1/2*3+1/3*4+...+1/2007*2008
=-(1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008)
=-(1-1/2008)
=-2007/2008
算式中的*为乘号

n*(n+1)=[n-(n+1)]/n(n+1)=-1/n(n+1)=1/(n+1)-1/n
所以1*2+2*3+3*4+...+2007*2008
=(1/2-1)+(1/3-1/2)+(1/4-1/3)+……+(1/2008-1/2007)
=1/2008-1
=-2007/2008