名校
解题方法
1 . 数列
满足
则称数列
为下凸数列.
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
,其中
,
分别是公比为
,
的两个正项等比数列,且
,证明:
是下凸数列且不是等比数列;
(3)若正项下凸数列的前
项和为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0bee75d4d83c0b76421fd87113e4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f67fc95a626251da11649acb5e1706f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c340d7d093dd4a275ffea4b87cd26827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c171ff5c2728e7cf00a88f88de14f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755d7aa870e2f199d6c12264fc9be86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若正项下凸数列的前
![](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/0002f427eded1721f43d60dd0fd3ffe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd419dc0a6580ab97777b2cb8fd7cded.png)
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4卷引用:2024届湖北省高三普通高中5月联合质量测评数学试卷
2 . 对于正整数m,n,存在唯一的自然数a,b,使得
,其中
,我们记
.对任意正整数
,定义
的生成数列为
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874689ac8a6f70ecd93aa1aaf7d626f6.png)
.
(1)求
和
.
(2)求
的前3项.
(3)存在
,使得
,且对任意
成立.考虑
的值:当
时,定义数列
的变换数列
的通项公式为
当
时,定义数列
的变换数列
的通项公式为
若数列
和数列
相同,则定义函数
,其中函数
的定义域为正整数集.
(ⅰ)求证:函数
是增函数.
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad12b60594a6408ccc237cad2880088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff38a5b95f1fb452d87fce9c80b1249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574aa06d3d4f9952157c60ec8f40b839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5914cd027a87542e12cfb0c92c0aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874689ac8a6f70ecd93aa1aaf7d626f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dbb663375b927f3c00d1be3fda1508.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37dbd8745cf6246eea337a1bf91258c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87dc8de41005802093ae66c08f46a7a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926145a2b2232a88ceed6e69dc050265.png)
(3)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623ebc0f0eba98e8f63b7cd982c11009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8144524289a76dadf88c02976acea2db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf0ce448d146abfcd0bd689b925d168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c20d94765a05ee86edf370dd64fcff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5914cd027a87542e12cfb0c92c0aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d054e320d843bf0ca4a620519f75ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8121a889da1f3ecbecd5387a9473c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98b98330b62847c220ab2f127e11391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5914cd027a87542e12cfb0c92c0aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d054e320d843bf0ca4a620519f75ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf19212dd24556423636ce37034cdf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d054e320d843bf0ca4a620519f75ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96dbc1106da9238ec6300e13ca3d9b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46498efb2e485c1172abe2189e498613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88ba8e1dc91318d8a9e1856d8ae080e.png)
(ⅰ)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88ba8e1dc91318d8a9e1856d8ae080e.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee5e2ada7f1e99bf68508d21b8f6fb7.png)
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3 . 若数列
在某项之后的所有项均为一常数,则称
是“最终常数列”.已知对任意
,函数
和数列
满足
.
(1)当
时,证明:
是“最终常数列”;
(2)设数列
满足
,对任意正整数
.若方程
无实根,证明:
不是“最终常数列”的充要条件是:对任意正整数
,
;
(3)若
不是“最终常数列”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc6de641322c6aeb24e0bbd875e65b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3980f4d5c5ec0f551d7a3c3c0b5ffdc7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b26218ecae19cc13017d561c01d69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36737370e7f4231ebdd27c957f47f45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8f2cc86844dc647bfb33344781e75a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66c77ea288be5bfb4445a76a2429aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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4 . 若无穷数列满足
,则称数列
为
数列,若
数列
同时满足
,则称数列
为
数列.
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b12e5ecd81639f10f291240e384ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b5274263f066a66515cca40ca6af24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a24dc73f12d72a1a01e693f7f11814c.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8321dab9d32a7adeb315561309d1d8cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd7db94da6a1d4a0b1ee0cac227e4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4acfdca1f3bb06d2b56b57339eabef5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
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5 . 已知数列
的前n项和为
,且
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31fb9cdc11d44c3dcab0488366ad458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6691617159667fcfc3f6ce9146cd075a.png)
A.当![]() ![]() | B.![]() |
C.数列![]() ![]() | D.当![]() ![]() |
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名校
解题方法
6 . 已知数列
为有穷正整数数列.若数列A满足如下两个性质,则称数列A为m的k减数列:
①
;
②对于
,使得
的正整数对
有k个.
(1)写出所有4的1减数列;
(2)若存在m的6减数列,证明:
;
(3)若存在2024的k减数列,求k的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed25314606b875ae6cdfa2d073c73c85.png)
②对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ae1214cc78e72fb613d7e649bc27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b3392579424244c50ddf416ee3434d.png)
(1)写出所有4的1减数列;
(2)若存在m的6减数列,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409ce4e6aa8638fe5880009dbb732f7.png)
(3)若存在2024的k减数列,求k的最大值.
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|
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9卷引用:北京市通州区2024届高三上学期期末摸底考试数学试题
北京市通州区2024届高三上学期期末摸底考试数学试题江西省赣州市南康中学2024届高三“九省联考”考后模拟训练数学试题(一)安徽省合肥一六八中学2024届高三“九省联考”考后适应性测试数学试题(二)2024届广东省新改革高三模拟高考预测卷一(九省联考题型)数学试卷(已下线)(新高考新结构)2024年高考数学模拟卷(三)(已下线)信息必刷卷01湖南省长沙市雅礼中学2024届高三下学期数学月考试卷(八)(已下线)数学(江苏专用01)山东省日照市五莲县第一中学2024届高考模拟预测(一)数学试题
7 . 17到19世纪间,数学家们研究了用连分式求解代数方程的根,并得到连分式的一个重要功能:用其逼近实数求近似值.例如,把方程
改写成
①,将
再代入等式右边得到
,继续利用①式将
再代入等式右边得到
……反复进行,取
时,由此得到数列
,
,
,
,
,记作
,则当
足够大时,
逼近实数
.数列
的前2024项中,满足
的
的个数为(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4cdd6f27334444c1884876b9e4cfe6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4174abb8a26d35b8df3bd4f30f431760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c2257b811f2f2b7bc912fc931c4a896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd810b777ea7c810453b560c078fe26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f302219f23caefd077370c29e557cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a74d79db6d58b2bfdb021d891cd822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b162b6248fba84ebaeb621f3dbe874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c07829bdcf009a84715f32c6784542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5237ae4a60796b4257e52a2c487c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63152e764f4f11e43d2895e07ea11bb.png)
A.1007 | B.1009 | C.2014 | D.2018 |
您最近一年使用:0次
2023-12-02更新
|
1091次组卷
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4卷引用:广东省2024届高三上学期11月统一调研测试数学试题
广东省2024届高三上学期11月统一调研测试数学试题重庆市北碚区缙云教育联盟2024届高考零诊数学试题江苏省南京市南京师大附中2024届高三寒假模拟测试数学试题(已下线)专题04 数列及求和(分层练)(四大题型+14道精选真题)
名校
8 . 已知
和
是各项均为正整数的无穷数列,如果同时满足下面两个条件:
①
和
都是递增数列;
②
中任意两个不同的项的和不是
中的项.
则称
被
屏蔽,记作
.
(1)若
,
.
(i)判断
是否成立,并说明理由;
(ii)判断
是否成立,并说明理由.
(2)设
是首项为正偶数,公差是
的无穷等差数列,判断是否存在数列
,使得
.如果存在,写出一个符合要求的数列
;如果不存在,说明理由;
(3)设
是取值于正整数集的无穷递增数列,且对任意正整数
,存在正整数
,使得
.证明:存在数列
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
则称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e46ecd051c92489c0d1d458932f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fef6975d285cabcf6be67c78f30d30.png)
(i)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
(ii)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b5bb0902c0daf52fe26a78a250b96f7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33f575cee1cddd9bbc34dcd592a4e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53442dcf82f93d94f20be6bf2c934cb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
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9 . 已知数列{
}为有限项数列,项数为
),若对任意
且
都有
|,则称{
}是“Ω数列”
(1)判断数列3,2,4,1,5,6和2,4,1,5,6是否是“Ω数列”(无需说明理由);
(2)已知{
}为项数
的等比数列,
,若{
}是“Ω数列”,求其公比q的取值范围;
(3)已知{
}是1,2,3,……,2022的一个排列,令
),若{
}和{bn}都是“Ω数列”,求
的所有可能值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c7c9ea3971a28408f53d299c20062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5516f33fabad3e4ef285fe740e858fe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7399fcd570d1de4057f2059759d18cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d62f9b6b1ae4aac8b8d7e480ced8b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)判断数列3,2,4,1,5,6和2,4,1,5,6是否是“Ω数列”(无需说明理由);
(2)已知{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afa6e51b3b27c3edb330cd7f190b6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)已知{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb4dba7ddd499538147b2359ae77d71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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解题方法
10 . 定义:符号
表示实数
、
、
中最大的一个数;
表示
、
、
中最小的一个数. 如,
,
.设
是一个给定的正整数
,数列
共有
项,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01199da4114511b6f3dced0fa4c50426.png)
,
.由
的取值情况,我们可以得出一些有趣的结论.比如,若
,则
.理由:
,则
.又
,
,于是,有
.试解答下列问题:
(1)若数列
的通项公式为
,求数列
的通项公式;
(2)若数列
满足
,
,求通项公式
;
(3)试构造项数为
的数列
,满足
,其中
是等比数列,
是公差不为零的等差数列,且数列
是单调递减数列,并说明理由.(答案不唯一)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225be414d59a022c9456348f56784318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d669c05de69c4e82327576e630e690de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd3c167e5fb2a5de897cbfededb1c75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d375f8080f4f9297d079a1556211118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d09f994198167ee71a261a20e437eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01199da4114511b6f3dced0fa4c50426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01042971eb25362b7a3f1c0643c4670d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658c3b3e72ac3a53632210c0c3de3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50a4b1e4f8b1d044300df7ef8205c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974ec2ba8cc5c3359a112eb7eef246a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5083a59d00ee26f5709202fa5344630c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974ec2ba8cc5c3359a112eb7eef246a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc35a1a6558499dbf8e368682bf46f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46148262daa2e1b3ef29f08701702c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e6b55263081a4c048677e232213189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5083a59d00ee26f5709202fa5344630c.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a6590a4909d70cbf8ed3e58e4978da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26219cb164d1ef457ce21fdf99376e5f.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3af24e0787167e622c0375b7a279a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d07b502d14c9431029a0645fa04cbca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)试构造项数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb2db37e079b735acc41ea3035139e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35d2715b9e36e8bb1b69d2f9fadb358.png)
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