已知[x]表示不超过x的最大整数(x∈R),如:[-1.3]=-2,[0.8]=0,[3.4]=3,定义{x}=x-[x],则{20122013}

2025-06-24 17:42:52
推荐回答(1个)
回答1:

由题意可得,{

2012
2013
}=
2012
2013

20122
2013
=
(2013?1)2
2013
=
20132?2×2013+1
2013
=2011+
1
2013

∴{
20122
2013
}=
1
2013

同理可得,
20123
2013
=
(2013?1)3
2013
=20132?3×2013+3?
1
2013
=2013×2010+2+
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