1 . 设数列
满足
,证明:
存在且等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21296826c9f4a87c6355009da1738456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb3a970bf38d5616614fbc065edee88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023高三·全国·专题练习
2 . 设
,
,证明数列
的极限存在并求此极限.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b1b1656f6a79ebda39b4ca5e7428a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0144de0c82563c5b7f44142aeffe2d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
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3 . 已知首项为
的数列
,满足
(a为常数).当a确定后,数列
由其首项
确定,当
时,通过对数列
的探究,写出“
是有穷数列”的一个真命题.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ad17200020a867276f340a54e2bbf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
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4 . 函数
,定义数列
如下:
,
是过两点
、
的直线
与x轴交点的横坐标,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dceed2e7a0a44f06934d0262b6bbfac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0736457346c11dd6f458418a4f747ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ac05b70c1744e92f3ba0fe8bab6ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28066d6618fc0e7dc90a7a684bcb0927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76b2f304f94dd60a48ca4ca5142a765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
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5 . 已知数列
中,
,求数列
的通项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff6fd1ce568fab4321b979e38a396d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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6 . 已知数列
满足
,
,求
.
![](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/1557965107a5d6573a2db0bf041679da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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2023高三·全国·专题练习
7 . 已知数列
的递推公式
,且首项
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05c4fec4a250ce9aa564fe83daed817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8945f021bf1969bcedd820f8ae5da1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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8 . 已知数列
中,
,
,求
的通项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23093a3f4c23494a943e3957596fee92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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9 . 已知数列{an}中,a1=3,
,求{an}的通项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25afba858439b055a604524813a6a7d.png)
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10 . 已知数列{an}中,
,
,求{an}的通项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb31f779599e9237468f96c81f05d4dd.png)
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