解题方法
1 . 已知正项数列
的前
项和为
,且满足
.
(1)求数列
的通项公式;
(2)求证:当
时,
.
![](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/6ea02313b5717516efb39fbcb670a5b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da813d9be452e2018e3312e57344f28.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ba0fa19d33a3284a237da669240b54.png)
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2024-03-23更新
|
345次组卷
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2卷引用:第六届高一试题(初赛)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
2 . 在
平面上有一系列的点
,对于正整数
,点
位于函数
的图象上,以点
为圆心的
与
轴相切,且
与
又彼此外切,若
,且
.
(1)判断数列
是否为等差数列;
(2)设
的面积为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d433859a47dd969e3904d3e9d16782ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991df64879833b7dbb0477fd75de7df5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b572c2c8262bb7bf6a8c9cdf1ebead22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b572c2c8262bb7bf6a8c9cdf1ebead22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83258693b38108f4899207752b2e38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee96afbd98ac32680e63b0b599ae6b5a.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3100ae0145d424c88cf5cf7c0e394241.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b572c2c8262bb7bf6a8c9cdf1ebead22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1772e134179df9a7bbaddf91ab7e5b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b537784495df88e497bf12a749d6e7.png)
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3 . 已知圆
过定点
,圆心
在抛物线
上运动,
为圆
在
轴上截得的弦.
(1)试判断
的长是否随圆心
的运动而变化.并证明你的结论;
(2)当
是
与
的等差中项时,抛物线
的准线与圆
有怎样的位置关系?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88523c036b67b0a81238e5b8c4609d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a9a1832264917c6e730fdce7f599a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c388f1f7160d3397610633dfde015fa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c19fa4cd646f4d877c3e58cc346651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146c403de6b5780cd03e25c775b806c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
名校
解题方法
4 . 各项不为0的数列
满足
,且
.
(1)求证:数列
为等差数列;
(2)若
对任意
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/ea57eca4b72f73d23c3fed1bc61b414a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562bf10d55724c77204c6953c7fbf7e2.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8355941ad1ce719c3164c1c39bd5b448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-03-03更新
|
1657次组卷
|
5卷引用:湖南省湘西州吉首市2023年第二届中小学生教师解题大赛数学试题
名校
5 . 已知数列
的首项
,且
.
(1)求证:数列
是等比数列;
(2)设
,求使不等式
成立的最小正整数n.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237dee2723a87e96deabc09c32b2707b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c3a0aee147f923699f8aabd951fbbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98eed21ddd1128bf63f2417f868048e3.png)
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2022-03-06更新
|
1814次组卷
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4卷引用:黑龙江省鸡西实验中学2020-2021学年高中教师命题大赛数学试题
黑龙江省鸡西实验中学2020-2021学年高中教师命题大赛数学试题四川绵阳市2022-2023学年高三二诊模拟考试(3)理科数学试题河北省邯郸市大名县第一中学2023届高三下学期2月月考数学试题(已下线)4.3.1 等比数列的概念(同步练习)-【一堂好课】2022-2023学年高二数学同步名师重点课堂(人教A版2019选择性必修第二册)
6 . 已知数列
中,
,
.正项等比数列
的公比
,且满足
,
.
(1)证明数列
为等差数列,并求数列
和
的通项公式;
(2)如果
,求
的前n项和为
;
(3)若存在
,使
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ac9d17bc8f166fc3894bf865ad6a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21cfd1ad0f4254be1d88c6577b6bbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90d19bcd582ed71cde0f18027174459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e3824ddd2210bd1e6313ad11dc8b13.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102abb18c888eb23d40708b97de140ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c39de50ed2f805d9c28aa7aadc46fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066141ba294715e4e725d59acfb85caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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7 . 已知
为数列
的前n项和,且
;数列
是各项均为正数的等差数列,
,4,
成等比数列,且
.
(1)求数列
和
的通项公式;
(2)若
,证明
.
![](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/18bb7c1d0429dbea3455011f99013350.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a79c23429da6d3e02f63a83541529a3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fab3af5f17a571a697ff0770fd8df2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f43f25cf6e03d904e300e8040bf9d96.png)
您最近一年使用:0次
2022-04-24更新
|
820次组卷
|
2卷引用:2023年全国中学生数学能力测评(终评)高三年级组试题
8 . 成等差数列的三个正数的和等于15,并且这三个数分别加上2、5、13后成为等比数列{bn}中的b3、b4、b5.
(Ⅰ)求数列{bn}的通项公式;
(Ⅱ)数列{bn}的前n项和为Sn,求证:数列{Sn+
}是等比数列.
(Ⅰ)求数列{bn}的通项公式;
(Ⅱ)数列{bn}的前n项和为Sn,求证:数列{Sn+
![](https://img.xkw.com/dksih/QBM/2017/1/6/1619444287930368/1619444288266240/STEM/fb869952a2da4844bbb954ac11b6da73.png)
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2016-12-03更新
|
2749次组卷
|
12卷引用:2013-2014学年湖北武汉蔡甸区第二中学高一下六科竞赛理科数学试卷
2013-2014学年湖北武汉蔡甸区第二中学高一下六科竞赛理科数学试卷2013-2014学年湖北武汉蔡甸区第二中学高一下六科竞赛数学文试卷2011年普通高等学校招生全国统一考试文科数学(湖北卷)2016-2017学年湖北宜昌葛洲坝中学高二文上期中数学试卷2016-2017学年河南省濮阳市高二上学期期末考试数学(理)试卷2016-2017学年河南省濮阳市高二上学期期末考试(A卷))理数试卷安徽省滁州市定远县育才学校2017-2018学年高一(普通班)下学期第三次月考数学试题【全国校级联考】贵州铜仁伟才学校2017-2018学年高一3月份月考数学试题云南省普洱市景东彝族自治县第一中学2019-2020学年高二下学期期中考试数学(理科)试题2016-2017学年河南省濮阳市高二上学期期末考试(A卷)文数试卷2016-2017学年河南省濮阳市高二上学期期末考试数学(文)试卷(已下线)天津市河西区2023-2024学年高二上学期期末质量调查数学试卷
11-12高三上·河南洛阳·期末
名校
9 . 设数列
的前
项和
满足:
,等比数列
的前
项和为
,公比为
,且
.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,求证:
.
![](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/8416d8f3b0044d515238a2cbb8164000.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9dfaeae03d5f5185b513de8bbb8e54.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc948ddd475d926a291c6b5eaa56da9f.png)
您最近一年使用:0次
2016-11-30更新
|
901次组卷
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7卷引用:广西陆川县中学2016-2017学年高二下学期知识竞赛数学(理)试题
广西陆川县中学2016-2017学年高二下学期知识竞赛数学(理)试题(已下线)2011届河南省洛阳市高三上学期期末考试理科数学(已下线)2011-2012学年山东省淄博一中高三上学期期末考试理科数学(已下线)2012届河北省衡水中学高三下学期二调考试理科数学试卷(已下线)2015届山西省太原五中高三10月月考文科数学试卷辽宁省抚顺市第一中学2019-2020年高三上学期期中数学(文)试题2020届辽宁师范大学附属中学高三上学期第二次考试(期中)数学(理)试题