解题方法
1 . 已知数列
的前
项和为
,且满足
,若数列
的前
项和
满足
恒成立,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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e7d0c282cd14c00ec4e3ff544b2b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b191044f5c024f377d999910b78b422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6688cb3e2287a6467a07c9dc82c43c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-08-27更新
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4卷引用:重庆市北碚区2022-2023学年高二上学期10月月考数学试题
名校
解题方法
2 . 如图,
是一块半径为1的圆形纸板,在
的左下端剪去一个半径为
的半圆后得到图形
,然后依次剪去一个更小的半圆(其直径为前一个前掉半圆的半径)得到图形
,记纸板
的周长为
,面积为
,则下列说法正确的有( )
![](https://img.xkw.com/dksih/QBM/2023/3/20/3198746959151104/3199963857502208/STEM/78a1c903c9294812a5e4d589ce802f13.png?resizew=499)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee2950b023f589d98b78160e791d9d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a2d3cd8e283ae9d04bee5ab2e0895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://img.xkw.com/dksih/QBM/2023/3/20/3198746959151104/3199963857502208/STEM/78a1c903c9294812a5e4d589ce802f13.png?resizew=499)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 已知数列
满足
,且
,则
中整数项的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a689b9366e89d09fceb573ff8afe2732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b07ca1eda3f94ad324236181b5f00c2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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4 . 已知数列
满足
,
,且
设
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8700d361a14772a8b3e4d3331f8ce24d.png)
_________
.
![](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/c415038439c063a0bc2a24012338078c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cd015d0960c5a2ac0e74b1400cf937.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/6a3f1f8813adcedd56b471961b2ad6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8700d361a14772a8b3e4d3331f8ce24d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c613d9c4f2baadcad70552390da2a403.png)
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2022-03-23更新
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534次组卷
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6卷引用:重庆市西南大学附属中学校2021-2022学年高二下学期第三次月考数学试题
重庆市西南大学附属中学校2021-2022学年高二下学期第三次月考数学试题重庆市西南大学附属中学校2021-2022学年高二(广延班)下学期第三次月考数学试题(已下线)4.3.2.1 等比数列的前n项和(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)(已下线)4.2 等比数列(第2课时)(六大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)四川省成都市成华区某校2023-2024学年高二下学期4月月考数学试题(已下线)【练】 专题2 构造数列问题
名校
解题方法
5 . 设数列
满足
,数列
的前
项和为
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a324ac0c12b4c49ab1f1afbce3a86592.png)
(1)求证:数列
为等差数列,并求
的通项公式;
(2)设
,若对任意正整数
,当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6084004a91a41ef56e7621714fa2687.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a324ac0c12b4c49ab1f1afbce3a86592.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82c65a855b1eed9c43e6829f6c3bffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a5da070ebb3fa29e0d7b402db804b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6de235c7c5205eb3d81109f04abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51d58e0f1ded5bd4d223c6e620069de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2022-02-22更新
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4卷引用:重庆市西南大学附属中学校2021-2022学年高二(广延班)下学期第三次月考数学试题
名校
6 . 设
,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d0fad3897651e493323dbcca2102f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eea9a0ba2b2454020fcb66c58478a48.png)
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2021-09-10更新
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3卷引用:重庆市西南大学附属中学校2020-2021学年高二下学期第四次月考数学试题
重庆市西南大学附属中学校2020-2021学年高二下学期第四次月考数学试题(已下线)专题07 基本不等式压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)2.1.2基本不等式
7 . 已知椭圆
的两个焦点
,
与短轴的一个端点构成一个等边三角形,且直线
与圆
相切.
(1)求椭圆
的方程;
(2)已知过椭圆
的左顶点
的两条直线
,
分别交椭圆
于
,
两点,且
,求证:直线
过定点,并求出定点坐标;
(3)在(2)的条件下求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638c8ebe4d2e418f1783269f71ef3826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74230ddd227bcf7c4efe67781d1c3203.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)在(2)的条件下求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
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2020-02-09更新
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698次组卷
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4卷引用:重庆市北碚区西南大学附属中学校2019-2020学年高二上学期期末数学试题