数列｛an｝中,a（n+1）*an=a（n+1）-1,且a2010=2,则前2010项的和等于

a(n+1)*an=a(n+1)-1a2010*a2009=a2010-1,a2009=1/2a2009*a2008=a2009-1,a2008=-1a2008*a2007=a2008-1,a2007=2a2007*a2006=a2006-1,a2006=1/2……a(3k)=1/2a(3k-1)=1a(3k-2)=2……a3=1/2a2=-1a1=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