1 . 将正整数
填入
方格表中,每个小方格恰好填1个数,要求每行从左到右10个数依次递减,记第
行的10个数之和为
. 设
满足:存在一种填法,使得
均大于第
列上的10个数之和,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deacb2d14b3b685334af74c9eb08e708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23f3b42cd6069f0e461035e76459ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aba753aa5e77c45b0d328c036a954a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e72518ba0d330df05786f6c48db9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77efd8c62dacd2212c3ff5db6b02a5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2 . 已知数列
满足
,对每个正整数
,有
或
.如这个数列可以为1,2,4,6,10….
(1)若某一项
为奇数,且不为3的倍数,证明:
;
(2)证明:
;
(3)若在
的前2015项中,恰有t个项为奇数,求t的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169498a7be9ef8b2a8c7b828d612722d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e40ed9ff04566921c6a1291eed08fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a404164c8d199f60d183a59b3647cc.png)
(1)若某一项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef3d144e7d714ee1b2638ede17709de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f4045b9f7cc8d35ea1c7681f90b965.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfee291b904a5f94cf2e00600d15839.png)
(3)若在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
您最近一年使用:0次
3 . 求1,2,···,n的排列
的个数,使得
对正整数k=1,2,···,n成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3413aee76d321d038d9628c95ad6e2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8942fd3e92278aee512b3f1f711282.png)
您最近一年使用:0次