名校
1 . 设满足以下两个条件的有穷数列
为
阶“期待数列”:①
;②
.
(1)若等比数列
为
阶“期待数列”
,求公比
;
(2)若一个等差数列
既是
阶“期待数列”又是递增数列
,求该数列的通项公式;
(3)记
阶“期待数列”
的前
项和为
,求证;数列
不能为
阶“期待数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d02a8555da4dbbc7820a50a95b071ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa0fca4198a6d5c5b76e5e1716dc4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39aa494487b73dbac3d6b868d822fddd.png)
(1)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5631bc01b998a4b3fabd9e131699dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1306375a0fec4eb4bf3f07992f6716e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)若一个等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5631bc01b998a4b3fabd9e131699dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1306375a0fec4eb4bf3f07992f6716e.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45581140d4687ff796b7cc53609702e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea210b22ee669a90173c4bd61c39596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500c42aa6116832f6ef1fe41d3d214bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
2 . 已知
是数列
的前
项和,对任意
,都有
;
(1)若
,求证:数列
是等差数列,并求此时数列
的通项公式;
(2)若
,求证:数列
是等比数列,并求此时数列
的通项公式;
(3)设
,若
,求实数
的取值范围.
![](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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4faa5d8f3b8d5f59910ef3e885abe4fc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46db680bc60929939e0f09990c03583e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac5c639aa5cd63ab86b2b0d9a23c998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6788d3dbbd2d5f865db8d414375339e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ba3d72887756e8d222e0e3ae6aff5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75330ac9e51cdef4bc61012551e1d00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2019-12-08更新
|
766次组卷
|
3卷引用:2018年上海市复旦附中高三5月三模数学试题
名校
3 . 已知数列
和
满足
,
,
.
(1)证明:
是等比数列,
是等差数列;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee423d15df9804185bf5242e75f501cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d807a81b4f3c1503bc8447f437bf91c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326a11bac583ee0eda8ebea723c103e2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec12a9a60f82467bf7bf834a9a9b1f7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a9cb389ad8e9aa57d822096810ea1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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9-10高三·上海·阶段练习
4 . 已知数列
中,
且点
在直线
上.
(1)求数列
的通项公式;
(2)若函数
,求函数
的最小值;
(3)设
表示数列
的前
项和.试问:是否存在关于
的整式
,使得
对于一切不小于
的自然数
恒成立? 若存在,写出
的解析式,并加以证明;若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b47ecee651ae4b4ecf7a8a0bffd2535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e7d8fb05d18b61b51e70ff1abed7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26251f92a46b07a3bfe81394b6e502d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2851cb9ffb602b4cec7ccd01e35dd95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c1a72253f12e053bb095752c0355cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2851cb9ffb602b4cec7ccd01e35dd95.png)
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