原式=(1 -1/2)+(1/2 -1/3)+(1/3 -1/4)+...+(1/2007 -1/2008)
=1 -1/2 +1/2 -1/3 +1/3 -1/4 +...+1/2007 -1/2008
=1 -1/2008
=2007/2008