1 . 求n位十进制数中包含偶数个3的数的个数.
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2 . 解方程组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44aa87e89ab9ff4bd1621f80abc68ac.png)
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3 . 已知数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f108d4cbb79fbc793f2dfc9209b9436d.png)
,
,求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f108d4cbb79fbc793f2dfc9209b9436d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf8197e4f3fd18815045d29c357a863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ed8e81641e04fad73ddfe81d26a871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
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4 . 在数列
中,已知
.
(1)若
,求
.
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385e1e22a5aa983b7684abefd599543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f4b7994a7b117342ed563c03388a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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名校
解题方法
5 . 已知函数
,数列
的前
项和为
,且满足
,则下列有关数列
的叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307bb5726473ed17fc82d14215f435f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/a27342dd38781f697127de9142861639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6 . 组合数学中有一著名问题——Hanoi问题:n个圆盘依其半径大小,从下而上套在A柱上,如图1所示.每次只允许取一个移到B柱或C柱上,而且不允许大盘放在小盘上方.问若要求把A柱上的n个盘移到C柱上要移动多少次(只有A,B,C三根柱子可用).
![](https://img.xkw.com/dksih/QBM/2023/5/22/3243098679615488/3245146346930176/STEM/11116fded3e84eb3a9841659f8027ec4.png?resizew=131)
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2023高三·全国·专题练习
7 . 设数列
满足递推关系
且有初始值
,
,求
的一般表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6d6661619bb233ec6db989fb47f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489340c9a2d70c00bae13b7018cad448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2023高三·全国·专题练习
8 . 斐波那契数列指的是这样一个数列:
,
,当
时,
.学习了斐波那契数列以后,班长组织同学们体育课上做了一个报数游戏:所有同学按身高从高到低的顺序站成一排,第一位同学报出的数为1,第二位同学报出的数也为1,之后每位同学所报出的数都是前两位同学所报出的数之和.若班上一共有30位同学,且所报数为5的倍数的同学需要说出斐波那契数列的一个性质,则需要说性质的同学有( )个?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a404164c8d199f60d183a59b3647cc.png)
A.4 | B.5 | C.6 | D.7 |
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2023高三·全国·专题练习
9 . 设数列
满足
,
,
,
.
(1)当
时,判断数列
的单调性;
(2)数列
的极限.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249367d6afff4ce02da27595ea9b3db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee7ee534b94c5415a7f67f821e861fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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10 . 若数列
满足:
,
.
(1)是否存在无穷数列
满足:对任意
,有
,请举一例,并指出所举例中a的范围;若不存在请说明理由;
(2)是否存在无穷数列
满足:对任意
,有
,请举一例,并指出所举例中a的范围;若不存在请说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8916a7bfe149fe37e01325ad753aee.png)
(1)是否存在无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2798e1dcab1f7f0fe3b8a94b3cd6a88.png)
(2)是否存在无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1254070260067f8bf2fec39a7d0c8f1.png)
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