1 . 根据数列的通项公式填写下表:
1 | 2 | … | 10 | … | … | … | |||
… | … | 420 | … | … |
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2 . 设
,
.
(1)当
时,计算
的值;
(2)你对
的值有何猜想?用数学归纳法证明你的猜想.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eadc627a4f683cf1e4db5b3ee4516aa7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4967a0f83ec59ad5a74ce1c3653a2451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
(2)你对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
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3 . 试分别根据下列条件,写出数列
的前5项:
(1)
,
,
,其中
;
(2)
,
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e70b04fb4879fd9b98a103c793414c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d676517bbb3c12d5028540db285ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
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4 . 已知数列
的首项为
,递推公式为
,写出这个数列的前5项.
![](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/6aecfe37a0d535c4392864f5e61731b9.png)
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23-24高二上·全国·课后作业
5 . 写出下面数列的前5项:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9579ce08a81ecb76e77c666ade0e4709.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823b2fcd0fbf3ba96d56276e2ae298ac.png)
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23-24高二上·全国·课后作业
6 . 写出下列数列的前5项:
(1)
,
;
(2)
,
;
(3)
,
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb8f0db1b16bff4310b82e06006562.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef12bf256807698ffa9e78ccde978273.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c13071fd55a570eefcc86dc9249d1e.png)
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23-24高二上·全国·课后作业
7 . 根据递推公式和初始条件
,出数列
的前5项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b83e5586bd9a6038f6f7667c81d7d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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21-22高二·江苏·课后作业
8 . 根据数列
的通项公式
,写出它的前4项及第
项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609c795a6b2c39b9fba2c57638693bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
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21-22高二·江苏·课后作业
解题方法
9 . 已知数列
的通项公式是
.
(1)写出这个数列的前5项,并作出它的图象;
(2)这个数列中有没有最小的项?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4da433938307d800f84a1471a26503.png)
(1)写出这个数列的前5项,并作出它的图象;
(2)这个数列中有没有最小的项?
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20-21高二·全国·课后作业
10 . 已知
中,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1f7536ff4ed7450fabf9db859784a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eed39c7d611309b01476c15ab242308.png)
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