数学找规律:1/2*3+1/3*4+1/4*5+1/5*6.+1/2007*2008=?

1/2*3+1/3*4+1/4*5+1/5*6。+1/2007*2008
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+。。。+(1/2007-1/2008)
=1/2-1/2008
=1003/2008