2011·北京东城·一模
1 . .对于n∈N*(n≥2),定义一个如下数阵:
,其中对任意的1≤i≤n,1≤j≤n,当i能整除j时,aij=1;当i不能整除j时,aij=0.设
.
(Ⅰ)当n=6时,试写出数阵A66并计算
;
(Ⅱ)若[x]表示不超过x的最大整数,求证:
;
(Ⅲ)若
,
,求证:g(n)﹣1<f(n)<g(n)+1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa52eb1f953450ed61379b31cb95d69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ca0f5d9d30acf82a6a81e0cace4cbb.png)
(Ⅰ)当n=6时,试写出数阵A66并计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443bee875d6e97bf14935e0cd3e58e52.png)
(Ⅱ)若[x]表示不超过x的最大整数,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ab5f5cadfb45b1436c7877f80993b.png)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3ae50f4a6cd489272e3cc0dbbd9df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795946aca112d97e28b81221bd9a8ae1.png)
您最近一年使用:0次