对于数列,若集合
为有限集,则称数列
为“好数列”.若“好数列”
满足
,则
22-23高二上·江苏盐城·期末 查看更多[2]
更新时间:2023-01-13 18:09:09
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解题方法
【推荐2】已知数列
满足
,若
,则数列
的首项的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a47df2d9dfb1e96d8888e18f2e59f48f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2798e1dcab1f7f0fe3b8a94b3cd6a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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【推荐1】记
为不超过实数
的最大整数,例如,
,
,
.设
为正整数,数列
满足
,
,现有下列命题:
①当
时,数列
的前3项依次为5,3,2;
②对数列
都存在正整数
,当
时总有
;
③当
时,
;
④对某个正整数
,若
,则
.
其中的真命题有____________ .(写出所有真命题的编号
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/5b925d162bfc4a318451bad1de9ad8ad.png?resizew=23)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/ee1f89affe794fe28a117f4609b51d9c.png?resizew=14)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/28f3976fd0e74dcfa740282a0c341bd7.png?resizew=47)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/585434c31b274a3eb49fe551eb7c110e.png?resizew=54)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/31e2bd027744455983d7ad6b2278f8a7.png?resizew=74)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/4e4e78553d03415abc2b93bc28c798f1.png?resizew=14)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/3b4928d316ef4eabb5ddb44b63baadf0.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/c6f6a6dbfd564709871981504d79e9cf.png?resizew=42)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/afe2d5da14fa41dab475e950ae7ea768.png?resizew=166)
①当
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/6f139028b0714464a79f09f063c0e4e6.png?resizew=38)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/3b4928d316ef4eabb5ddb44b63baadf0.png?resizew=31)
②对数列
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/3b4928d316ef4eabb5ddb44b63baadf0.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/aa0c1e923f4c4bfca41504586d7ee39c.png?resizew=14)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/a6fd903d4ae44420b56481433e5ec9d8.png?resizew=38)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/697f7157508e423aa3561faa6f5f93cc.png?resizew=49)
③当
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/7010e667bfab43bdac2789b62e01af81.png?resizew=34)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/7f4c55d91a4f47b78d47b0509492088c.png?resizew=75)
④对某个正整数
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/aa0c1e923f4c4bfca41504586d7ee39c.png?resizew=14)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/307fd8cee4404a6da51acfd596455ca2.png?resizew=58)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037094400/STEM/3a599da3f566443f9ef3dd04bcd68a02.png?resizew=66)
其中的真命题有
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【推荐1】设
,关于
的方程
的四个实根构成以
为公比的等比数列,若
,则
的取值范围为______ .
![](https://img.xkw.com/dksih/QBM/2015/3/12/1572005271003136/1572005276688384/STEM/8bc47ed773c74172b7d557e6dd14a85b.png?resizew=53)
![](https://img.xkw.com/dksih/QBM/2015/3/12/1572005271003136/1572005276688384/STEM/027d06487b84471d99ad5b1b0cbd49cf.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2015/3/12/1572005271003136/1572005276688384/STEM/3e078bf1ea0f41ba98ecb916a4c27314.png?resizew=179)
![](https://img.xkw.com/dksih/QBM/2015/3/12/1572005271003136/1572005276688384/STEM/79a563d832994ebba80aaca202b7c72f.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2015/3/12/1572005271003136/1572005276688384/STEM/941698508805426eb0d738dd811df1cb.png?resizew=61)
![](https://img.xkw.com/dksih/QBM/2015/3/12/1572005271003136/1572005276688384/STEM/a86af4cb5a6e4b31b0ae8f410b0a5617.png?resizew=21)
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【推荐2】英国物理学家牛顿用“作切线”的方法求函数的零点时,给出的“牛顿数列”在航空航天中应用广泛.若数列满足
,则称数列
为牛顿数列.若
,数列
为牛顿数列,且
,
,数列
的前n项和为
,则满足
的最大正整数n的值为
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【推荐1】已知
是正项等比数列,
,且
,若
表示不超过
的最大整数(例如
,
)设
,则数列
的前
项和为
为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec47fa53ba40397c04631416f960f54d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7521add6393abf782a9d57c94863ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3efb7c56f45848f09a81db8785d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d0024c22d248668a379d8dd1b84cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d8811ce6cddf86019c5c84781ad0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05e0d43a6e2c47e03ad84915520b138.png)
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名校
【推荐2】学者森德拉姆(Sundaram)发现了一个有意思的素数筛法矩阵,这个矩阵后来在素数研究领域获得广泛应用.我们用
(
)表示矩阵中第i行第j列处的分量,这些分量之间满足如下递推关系:
,
,
,数表局部如下:
关于森德拉姆(Sundaram)素数筛法矩阵,有下列说法
①
; ②
;
③
; ④存在i,
使得
.
其中,所有正确说法的序号是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba1bbe411bc71bca016d3fd82352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8ad3cf001b89b9df5363d096eacee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6123377e52f8611dc24eccc0dc29bf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04230dc33504a3af9682bfcdb71b0921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/534a7166c49a9f39c31b5d92e66a5b42.png)
4 | 7 | 10 | 13 | 16 | 19 | … |
7 | 12 | 17 | 22 | 27 | 32 | … |
10 | 17 | 24 | 31 | 38 | 45 | … |
13 | 22 | 31 | 40 | 49 | 58 | … |
16 | 27 | 38 | 49 | 60 | 71 | … |
19 | 32 | 45 | 58 | 71 | 84 | … |
… | … | … | …… | … | … | … |
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10512e15a48cb2b27cc60a90086f94b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01804f36afe15f0327cc8ae450b6294e.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2abebbae7edc68681b50c47aafd9d1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cfbd6f249dc98fdabe20ec58fbc467c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b00503e90e7f627e9c85f76d195a54.png)
其中,所有正确说法的序号是
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