由题意可得,{
}=2012 2013
,2012 2013
∵
=20122
2013
=(2013?1)2
2013
=2011+20132?2×2013+1 2013
1 2013
∴{
}=20122
2013
1 2013
同理可得,
=20123
2013
=20132?3×2013+3?(2013?1)3
2013
=2013×2010+2+1 2013
2012 2013
∴
=20123
2013
2012 2013
∴{
}+{2012 2013
}+{20122 2013
}+…+{20123 2013
}20122012 2013
=
+1 2013
+…+2012 2013
+1 2013
2012 2013
=1×1006=1006
故答案为:1006