11-12高三·天津·阶段练习
1 . 已知数列
的相邻两项
是关于
的方程
的两根,且
.
(1)求证:数列
是等比数列;
(2)求数列
的前
项和
;
(3)设函数
,若
对任意的
都成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d514eb8dff80d4dc3f39de516b63b846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbeaa59cf76391392a5772c55aa7919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d6dd6774d18f0e37d02add8c39ea6a.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1f1146b05a9806adaa5a1ffdb3d51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c647ce39c059b9dec7fc67125431495f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2016-12-01更新
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1061次组卷
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7卷引用:2012届天津市天津一中高三第三次月考理科数学
(已下线)2012届天津市天津一中高三第三次月考理科数学(已下线)2013届湖南省五市十校高三第一次联合检测理科数学试卷(已下线)2013届山西省山大附中高三3月月考理科数学试卷(已下线)2013-2014学年江西新余市高二上学期期末理科A数学试卷2014-2015学年黑龙江佳木斯一中高一下学期期中数学试卷2014-2015学年江西省南昌市第十九中学高一下学期期中考试数学试卷天津市五校2019-2020学年高二上学期期末联考数学试题
2 . 已知曲线
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b26661c7e170b3da92eb42c84da457.png)
,从
上一点
作
轴的垂线,交
于点
,再从点
作
轴的垂线,交
于点
.设
,
,
(1)求
,
的坐标 ;
(2)求数列
的通项公式;
(3)记数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f5c00a4cb3fc3783b4abeb06fb4d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b26661c7e170b3da92eb42c84da457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014f3f1128f7d6a93a4ea34967b96c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178f804adbf58b3b48ca1e6de3c2fba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd9d64d968a4cb62d696c8ad1642eb23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c775fc62e7696028a9184e5212f0446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0873d9cdecbadf963e9fedcd4edec86.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153d172ee17295f0d6d60e891d3f6529.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/3cf4cea13f3c0a934a3be5a3d834774f.png)
![](https://img.xkw.com/dksih/QBM/2011/12/6/1570557903421440/1570557908967424/STEM/dca898e993214f328bf6c63826334f73.png?resizew=189)
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3 . 设数列
各项为正数,且
.
(Ⅰ)证明:数列
为等比数列;
(Ⅱ)设数列
的前
项和为
,求使
成立时
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb6947ca72c6ff23c1c7ca4160e5361e.png)
(Ⅰ)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c528dfc0f0a9f0037209ddd2630eea5.png)
(Ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81b99962c95aa5d0e573437a08b6dc7.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/7f2f6f1381e8ea1497f74cf930a8027d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2016-12-04更新
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3卷引用:四川省成都市龙泉第二中学2018届高三10月月考数学(文)试题
2012·河北张家口·一模
名校
4 . 已知等比数列
中,
,公比
.
(1)
为
的前
项和,证明![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55ffc2ff30d2a1297d08e7c44bb397f.png)
(2)设
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e3fc803117ae94861839984a0afef4.png)
(1)
![](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/c55ffc2ff30d2a1297d08e7c44bb397f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d183b8009a281499b28f22bb5a1df66c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
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11卷引用:2012-2013学年河北省存瑞中学高一下学期第二次月考数学试卷
(已下线)2012-2013学年河北省存瑞中学高一下学期第二次月考数学试卷2016届宁夏银川市二中高三上学期统练二文科数学试卷(已下线)2012届河北省涿鹿中学高考预测试文科数学试卷(已下线)2013-2014学年安徽省安庆市外国语学校高一下学期期中考试数学试卷2014-2015学年四川省邻水中学高一下学期期中文科数学试卷专题11 数列(2)(已下线)专题18 等差数列与等比数列-十年(2011-2020)高考真题数学分项四川省达州市渠县中学2020-2021学年高二上学期期中数学理科试题(已下线)专题4.3 等比数列-2020-2021学年高二数学同步培优专练(人教A版2019选择性必修第二册)陕西省渭南市杜桥中学2020-2021学年高二上学期期中文科数学试题(已下线)4.3.2等比数列的前n项和(2)
12-13高三上·山东聊城·阶段练习
5 . 已知数列{an}的前n项和为 Sn
(n∈N*),且a1=2.数列{bn}满足b1=0,b2=2,
,n=2,3,….
(Ⅰ)求数列 {an} 的通项公式;
(Ⅱ)求数列 {bn} 的通项公式;
(Ⅲ)证明:对于 n∈N*,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e65f29cdfbf4b8cd002e0e0a752306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb477cb4fd6db76606a6f85150a661b6.png)
(Ⅰ)求数列 {an} 的通项公式;
(Ⅱ)求数列 {bn} 的通项公式;
(Ⅲ)证明:对于 n∈N*,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0f974ab5c330487609651c35c9927f.png)
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6 . 在数列
中,
,且已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f203ed29bff3fae2c00ddffec48f04c.png)
在
处取得极值.
(1)证明:数列是等比数列;
(2)求数列
的通项
和前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b752334e1a2744cad632074c456dee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f203ed29bff3fae2c00ddffec48f04c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e33d429e8ada5715145e94f25cd16f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(1)证明:数列是等比数列;
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
名校
解题方法
7 . 已知
是等差数列,其前
项和为
,
是等比数列,且
,
,
.
(Ⅰ)求数列
与
的通项公式;
(Ⅱ)记
,
,证明
(
,
).
![](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/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5a7a17a394e868e0acd1803a9ab795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da00560d18f576a37bcc21459698145f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b224a65a8f2d495d327e4a488c0dba1.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(Ⅱ)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4ed9d2c4f561c118ad7581fda564bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e98a2cb8bcf8604c83b02e78693eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153fb853cd99beec9e600a4eaf73fe8.png)
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3卷引用:天津市第二中学2021-2022学年高三上学期12月月考数学试题
8 . 已知数列{
}的首项为1,
为数列{
}的前n项和,
,其中q>0,
.
(Ⅰ)若
成等差数列,求数列{an}的通项公式;
(Ⅱ)设双曲线
的离心率为
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549b17fd03994ba73f3341b7189fc01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168d1aaf6b99875b3c5c84882978e364.png)
(Ⅱ)设双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e692bfc8107c4819e98af3f74c89db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f567549e66b339299dbf8369ab5812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17ceba8160ccefa3c4bccc749491dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7532aa134229978d1e36af60959d237.png)
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7卷引用:重庆市育才中学2020-2021学年高二上学期10月月考数学试题
重庆市育才中学2020-2021学年高二上学期10月月考数学试题2016年全国普通高等学校招生统一考试理科数学(四川卷精编版)(已下线)专题14 数列综合-五年(2016-2020)高考数学(文)真题分项(已下线)专题19 数列的求和问题-十年(2011-2020)高考真题数学分项(已下线)考点21 数列求和问题-2021年新高考数学一轮复习考点扫描(已下线)2016年全国普通高等学校招生统一考试理科数学(四川卷参考版)专题28数列解答题
名校
解题方法
9 . 已知数列{an}的前n项和Sn满足Sn=2an-n.
(1)求数列{an}的通项公式;
(2)设
,记数列{bn}的前n项和为Tn,证明:
(1)求数列{an}的通项公式;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c9dc190d0856e27a1cc225f766808e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc35cadd404e73a7c95cc49d417139cf.png)
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2016-12-04更新
|
916次组卷
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4卷引用:2015届浙江省嘉兴一中五校高三上学期第一次联考理科数学试卷
10 . 已知数列
中,
,
且
.
(1)证明数列
是等比数列;
(2)若
是数列
的前
项和,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65561c9a235cf5964f6e047a765ec9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2231950b845fe2ddec5f8734bce5ce98.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
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2016-12-03更新
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