解题方法
1 . 下表给出的是由n×n(n≥3,n∈N*)个正数排成的n行n列数表,
表示第i行第j列的数,表中第一列的数从上到下依次成等差数列,其公差为d ,表中各行中每一行的数从左到右依次都成等比数列,且所有公比相等,公比为
,若已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d124e935b168b9e8427b84c73a660e56.png)
(1)求
的值;
(2)求用
表示
的代数式;
(3)设表中对角线上的数
,
,
,……,
组成一列数列,设Tn=
+
+
+……+
求使不等式
成立的最小正整数n.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d124e935b168b9e8427b84c73a660e56.png)
![]() | ![]() | ![]() | … | ![]() |
![]() | ![]() | ![]() | … | ![]() |
![]() | ![]() | ![]() | … | ![]() |
… | … | … | … | … |
![]() | ![]() | ![]() | … | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1349e472ed309807306135794f152a7.png)
(2)求用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c639c7e5f1e7e7ee5d5ee2f30b155bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
(3)设表中对角线上的数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e84c30444f13d37ada78285dc4f83b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e11a5b70e1e2e685d1783a4707872e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f4b25db4e5f4a3743476ae088720fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c06519b37bebc4d638da4efa8a6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e84c30444f13d37ada78285dc4f83b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e11a5b70e1e2e685d1783a4707872e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f4b25db4e5f4a3743476ae088720fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c06519b37bebc4d638da4efa8a6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af0b4987e9b7716b36b5ca99b0db0f2.png)
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2016-11-30更新
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679次组卷
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3卷引用:广州省高州一中2009-2010学年高二学科竞赛(数学理)