名校
1 . 已知数列
满足:
,
.
(1)求数列
的通项公式;
(2)用适当的组合数形式表示
,并求数列
的前n项和
;
(3)若
,记数列
的前n项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c339234052548a53ce660908f38a1210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/511502df6b8ec9c25d96828fc51d953d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)用适当的组合数形式表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f4513dec8ddde108d2ad95aec92781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1a208706fe64c4a6709e9de5da2bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6107e08dbb5a23afbc981c699b22564.png)
您最近一年使用:0次
2 . 已知一列非零向量
满足:
,
.
(1)写出数列
的通项公式;
(2)求出向量
与
的夹角
,并将
中所有与
平行的向量取出来,按原来的顺序排成一列,组成新的数列
,
,
为坐标原点,求点列
的坐标;
(3)令
(
),求
的极限点位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1522e062601bd8cbf0e1dfb46dc99479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49b6a97015f79f0983d305aa983a88f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66261c618f9763e23dcb04a9771a86.png)
(1)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f57a446af44cbd1d45f1b2cdacb9c74.png)
(2)求出向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1522e062601bd8cbf0e1dfb46dc99479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2121e9cac7d80abd7c6a0c0de5c67a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf5f89d712057721347c9ad379f2bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d970a4c8abf3fe4da3382206086a6cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9884ed3079050c09acb96895f6d54a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c522b64b43282038d18aaa9ebf03f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc5d10484bd7ecd36924b654e80090d.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3934a18e0212a835cd4ca825150870f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62029dee4a794614a812552ae958a6f5.png)
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名校
3 . 已知:函数
,数列
对
,总有
;
(1)求
的通项公式;
(2)设
是数列
的前
项和,且
,求
的取值范围;
(3)若数列
满足:①
为
的子数列(即
中每一项都是
的项,且按在
中的顺序排列);②
为无穷等比数列,它的各项和为
,这样的数列是否存在?若存在,求出所有符合条件的数列
.写出它的通项公式,并证明你的结论;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910617443037769340f252e4efe21536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea88016f672b8f54901e457cceecca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d500d7b62f418a4bcd75ce718c8c5a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](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/a4373b0bead6e6acdd697c6693e7d4af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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4 . 对于任意的
,若数列
同时满足下列两个条件,则称数列
具有“性质
”.①
;②存在实数
使得
.
(1)数列
中,
,判断
是否具有“性质
”.
(2)若各项为正数的等比数列
的前
项和为
,且
,证明:数列
具有“性质
”,并指出
的取值范围.
(3)若数列
的通项公式
,对于任意的
,数列
具有“性质
”,且对满足条件的
的最小值
,求整数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc75a9da38151496ca2adce84a977b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a82cb73e7f26bb82fd03ba9818c625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若各项为正数的等比数列
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e934a2b626f5717fac725956984554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b70cbddf99b55a928e1b16ffce339b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0edbd6959f3236a6d3a7f81c849237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8191d51029a192d504bf1b736029f82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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