1 . 如果一个实数数列
满足条件:
(
为常数,
),则称这一数列 “伪等差数列”,
称为“伪公差”.给出下列关于某个伪等差数列
的结论:
①对于任意的首项
,若
则这一数列必为有穷数列;
②当
时,这一数列必为单调递增数列;
③这一数列可以是一个周期数列;
④若这一数列的首项为1,伪公差为3,
可以是这一数列中的一项;
⑤若这一数列的首项为0,第三项为-1,则这一数列的伪公差可以是
.
其中正确的结论是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefdef1490b9a57916b6fa249d8926d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①对于任意的首项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8bbb4a09e0ac86bbae46222a90841.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b177dbff01bdc85b90b0947ddefd33a.png)
③这一数列可以是一个周期数列;
④若这一数列的首项为1,伪公差为3,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071ff10740d0ef09e9b6ab0bf8a92283.png)
⑤若这一数列的首项为0,第三项为-1,则这一数列的伪公差可以是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea677602592c01538ecb303619d24fe.png)
其中正确的结论是
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2 . 我们把一系列向量
按次序排成一列,称之为向量列,记作
,已知向量列
满足:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0605d93f56eebf6f20df7d12f60a4b.png)
.
(1)证明:数列
是等比数列;
(2)设
表示向量
与
间的夹角,若
,对于任意正整数
,不等式
恒成立,求实数
的范围
(3)设
,问数列
中是否存在最小项?若存在,求出最小项;若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8f29baa5b51c3a590a9d1293573a62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a38e5d6578eccec4d2da37de80b885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a38e5d6578eccec4d2da37de80b885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/087af434bb9df4c28b96fdf0783bd080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0605d93f56eebf6f20df7d12f60a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd048fe3fbd6b0623f146a0ef9021e1.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16c067abe5852f5fe0ebd2a46b4c552.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ffa8be5a02790c6161c56b8e90db64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56be493b67953d5800a3e4a3166b4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d1899ef8c31d8ff1949a00e75b7228b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e3fde07e9d6c27f3404da487d8bb32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f2b502db3e2994c5a510ea82281934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c370af362fca8f999169eafce599ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
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2016-12-03更新
|
1504次组卷
|
2卷引用:江西省南昌市第二中学2017-2018学年高一下学期第一次月考数学试题
2011·广东揭阳·一模
名校
3 . 数列
首项
,前
项和
与
之间满足
.
(1)求证:数列
是等差数列;并求数列
的通项公式;
(2)设存在正数
,使![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e30b34d3ef33337e769109bcdcc381.png)
对任意
都成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4a643e34e4fe80e2e44d73798bb50e.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad83668ff336589f82a2cd04db9f9947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设存在正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e30b34d3ef33337e769109bcdcc381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbcd2d3551aaddbc071957c721ac0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2016-11-30更新
|
1595次组卷
|
7卷引用:江西省南昌市第十中学2020-2021学年高一下学期第二次月考数学试题
2014高三·全国·专题练习
4 . 已知Sn是数列{an}的前n项和,且an=Sn-1+2(n≥2),a1=2.
(1)求数列{an}的通项公式.
(2)设bn=
,Tn=bn+1+bn+2+…+b2n,是否存在最大的正整数k,使得
对于任意的正整数n,有Tn>
恒成立?若存在,求出k的值;若不存在,说明理由.
(1)求数列{an}的通项公式.
(2)设bn=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc19bd370858782426f32566b84cc35.png)
对于任意的正整数n,有Tn>
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e37a1ebab735e1d53c9e36625e9955.png)
您最近一年使用:0次