a(n+1)*an=a(n+1)-1
a2010*a2009=a2010-1,a2009=1/2
a2009*a2008=a2009-1,a2008=-1
a2008*a2007=a2008-1,a2007=2
a2007*a2006=a2006-1,a2006=1/2
……
a(3k)=1/2
a(3k-1)=1
a(3k-2)=2
……
a3=1/2
a2=-1
a1=2
s2010=[a1+a2+a3]+……+[a(3k-2)+a(3k-2)+a(3k-2)]+……+[a2008+a2009+a2010]
=[2-1+1/2]+……+[2-1+1/2]+……+[2-1+1/2] (共2010/3=670组）
=[3/2]*670
=1005