名校
解题方法
1 . 定义:若对
恒成立,则称数列
为“上凸数列”.
(1)若
,判断
是否为“上凸数列”,如果是,给出证明;如果不是,请说明理由.
(2)若
为“上凸数列”,则当
时,
.
(ⅰ)若数列
为
的前
项和,证明:
;
(ⅱ)对于任意正整数序列
(
为常数且
),若
恒成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9e587fa47050e45101bbfbfe129fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3adcc926ce1056eefbad88408820424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48407f815d07eb8b5dfa8d34b724512e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede85acd5056e2907a48131e71c45411.png)
(ⅰ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a62e059e03eda6884da213547097ed9.png)
(ⅱ)对于任意正整数序列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6f1287d0218a833f34a97a9db24cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e988e0b43c5730e1c104004514801d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c9507d571eb0de009f16f1837579f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-04-10更新
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