名校
解题方法
1 . 已知数列
中,
,且
,若存在正整数
,使得
成立,则实数
的取值范围为( )
![](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/53ca2cae224aae175d07a96cf95c9118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551b1fb748642c8e6b3deced91340b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-02-09更新
|
1148次组卷
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2卷引用:河北省沧州市2023届高三上学期12月教学质量监测调研数学试题
解题方法
2 . 已知无穷数列
满足:①
;②
(
;
;
).设
为
所能取到的最大值,并记数列
.
(1)若
,写出一个符合条件的数列A的通项公式;
(2)若
,求
的值;
(3)若
,求数列
的前100项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6b7c794c3329ca99a71eb07c4a7b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8d9def91c6734e75134ef49ba0418a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a21caee5b908cd571bf28d61be90aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228114fab3c07bc63978df7e2dc31953.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8faa0cc59f291d53f801546d5dabe6fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fa5e5f1551d40f96a03ca6975e68f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d00457e8d086f28ea1b24bd880c9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297bc58fc87efa1f15d7eb9b5eb42260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fb6fbf69268bc82274bc7ff03010c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51cf6e2a57173496d722a325ffd16af.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e35c9a35017d2fdcd10f76b4a776419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879ed18e2aaf5ef408be9e6ac8d9e30a.png)
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2022-05-30更新
|
1422次组卷
|
5卷引用:北京市东城区2022届高三下学期综合练习(三)数学试题
北京市东城区2022届高三下学期综合练习(三)数学试题(已下线)2022年新高考北京数学高考真题变式题13-15题(已下线)2022年新高考北京数学高考真题变式题19-21题北京卷专题18数列(解答题)(已下线)专题11 数列前n项和的求法 微点8 分组法求和
3 . 已知数列
中,
,若
,则下列结论中错误的是( )
![](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/d8a64aee90aed584681c3b924f8db03a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-05-26更新
|
1910次组卷
|
6卷引用:浙江省杭州高级中学2022届高三下学期5月仿真模拟数学试题
浙江省杭州高级中学2022届高三下学期5月仿真模拟数学试题(已下线)专题6-1 数列函数性质与不等式放缩(讲+练)-2(已下线)专题10 数列通项公式的求法 微点2 累加法(已下线)第三章 重点专攻二 不等式的证明问题(核心考点集训)(已下线)专题06 数列在高考中的考法(难点,十一大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
2022·全国·模拟预测
4 . 已知数列
满足
,
,
,数列
的前n项和为
,且
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640e40b1b87fdd9c8bee7c1a5bae78b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2adf14bea097284d798138dcb07b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cbac4858faac6c9ac77816d503ad46a.png)
A.![]() |
B.![]() |
C.数列![]() |
D.满足不等式![]() |
您最近一年使用:0次
2022-05-17更新
|
1544次组卷
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4卷引用:2022届高三普通高等学校招生全国统一考试数学押题卷(二)
(已下线)2022届高三普通高等学校招生全国统一考试数学押题卷(二)福建省莆田华侨中学2022-2023学年高二上学期期中考试数学试题湖南省湘西州吉首市2022年第一届中小学生教师解题大赛数学试题安徽省安庆市2023届安庆第一中学高考三模数学试题
5 . 从一个无穷数列
中抽出无穷多项,依原来的顺序组成一个新的无穷数列,若新数列是递增数列,则称之为
的一个无穷递增子列.已知数列
是正实数组成的无穷数列,且满足
.
(1)若
,
,写出数列
前
项的所有可能情况;
(2)求证:数列
存在无穷递增子列;
(3)求证:对于任意实数
,都存在
,使得
.
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec7667e8c3fd05a00e978da0880546c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e96fafcc7b7f783d436f853449208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(2)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)求证:对于任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f7ad6c588fd975c9bbe389fd37a058.png)
您最近一年使用:0次
6 . 投掷一枚硬币(正反等可能),设投掷n次不连续出现三次正面向上的概率为
.
(1)求
,
,
和
;
(2)写出
的递推公式,并指出增减性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
您最近一年使用:0次
解题方法
7 . 已知
是各项均为正整数的数列,且
,
,对
,
与
有且仅有一个成立,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff6de1ee895470114429ac01726f405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc16bb35c68f1cce33384bae08568ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/badffa63b1547fbc4263482d2f1b76e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2743997f5cf383858bd7c4db893f3128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994dee3ee1abb0f2f8b764177a04d2b1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
8 . 已知正整数数列
满足:
,
,
.
(1)已知
,
,求
和
的值;
(2)若
,求证
;
(3)求
的取值范围.
![](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/a55ef34345210312db273ab4981c40f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf89aa413e6db9a800fae7798718108e.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f86a8746a583f411fb73c6334eb27b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2367e607a23ebf82ed2b859aadd57952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efac4bb9d79292964399cb51379c6657.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
2021-03-22更新
|
1041次组卷
|
4卷引用:考向18 数列不等式-备战2022年高考数学一轮复习考点微专题(上海专用)
(已下线)考向18 数列不等式-备战2022年高考数学一轮复习考点微专题(上海专用)浙江省2021届高三4月份高考数学模拟试题(10)上海市建平中学2021届高三下学期开学考试数学试题(已下线)模块九 数列-2
名校
9 . 记
为不超过实数x的最大整数,例如:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc7e606533e84b25701a06c7ed4a66c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06209398c08b78d85dd36e43e6314c4.png)
,设a为正整数,数列
满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8702ac0fd9676c9a5c9ce20c71c4dd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4b0cd80d95662729de6af4fa5add73.png)
,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k,当
时,总有
;
③当
时,
;
④对某个正整数k,若
,则
;
其中的真命题个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc7e606533e84b25701a06c7ed4a66c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06209398c08b78d85dd36e43e6314c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b729161007e4c37743f6f9408dee1218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8702ac0fd9676c9a5c9ce20c71c4dd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4b0cd80d95662729de6af4fa5add73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fc82353331abee0828dee9b38c08f2.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab839d8569171afab5ed55c22013aa72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
②对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fef5f2a4235817fb704d29e08766e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28eb741935c8eaaaeb8fa68f674ee10b.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd0de9946f770bdc7202847a035c05f.png)
④对某个正整数k,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc629d8dee9b3aceaf7effe90bce3e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1a4efd1038d401a1bd375f5f574a97.png)
其中的真命题个数为
A.4 | B.3 | C.2 | D.1 |
您最近一年使用:0次
名校
10 . 已知以
为首项的数列
满足:
.
(1)当
时,且
,写出
、
;
(2)若数列
是公差为-1的等差数列,求
的取值范围;
(3)记
为
的前
项和,当
时,
①给定常数
,求
的最小值;
②对于数列
,
,…,
,当
取到最小值时,是否唯一存在满足
的数列
?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b020f45693cb1f85ed1b793a60f86a14.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c492ef0c41f7a2f4c15fb27df44a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728e3a4f5e54524bbabe2a4eda052c7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ad75ec865e9e64aafe281d4dd91899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/d1bae03ee4ac75dacfb026290e4207dd.png)
①给定常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7c8f4a4bc521392c407efb60d9bdc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4a600ed8be6911a37d279bd23dd798.png)
②对于数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eed39c7d611309b01476c15ab242308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7581cdb1703687ff550247f6af8a985a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2019-10-23更新
|
496次组卷
|
3卷引用:4.3利用递推公式表示数列(第2课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件
(已下线)4.3利用递推公式表示数列(第2课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件上海市交通大学附属中学2019-2020学年高二上学期9月月考数学试题上海市大同中学2023-2024学年高一下学期5月月考数学试题