名校
解题方法
1 . 已知函数
,数列
的前
项和为
,且满足
,则下列有关数列
的叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307bb5726473ed17fc82d14215f435f4.png)
![](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/a27342dd38781f697127de9142861639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
2 . 数列
满足
,则以下说法正确的个数( )
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257beff965e09fcb5649a0239df59205.png)
②
;
③对任意正数
,都存在正整数
使得
成立
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6190b53b3c2362929b165929427a535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6098e30182e2e692702b1d1c55ec267c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257beff965e09fcb5649a0239df59205.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584363593b8fecb03a88569fea264a66.png)
③对任意正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfe1f24ce4272715e5b4fdf223e80fa.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6190b53b3c2362929b165929427a535c.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2022-06-23更新
|
1732次组卷
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13卷引用:浙江省杭州市桐庐中学2020-2021学年高三上学期12月精准测试数学试题
浙江省杭州市桐庐中学2020-2021学年高三上学期12月精准测试数学试题浙江省台州市六校2020-2021学年高三上学期期中联考数学试题(已下线)【新东方】412(已下线)4.4 数学归纳法-2021-2022学年高二数学链接教材精准变式练(苏教版2019选择性必修第一册)(已下线)专题7.6 数学归纳法(练)- 2022年高考数学一轮复习讲练测(新教材新高考)(已下线)2022年全国高考乙卷数学(理)试题变式题17-20题四川省成都市第七中学2023届高三上学期零诊模拟检测理科数学试题四川省成都市第七中学2023届高三上学期零诊模拟检测理科数学试题(已下线)专题06 数列(文理)(已下线)2022年全国高考乙卷数学(理)试题变式题1-4题(已下线)4.4 数学归纳法-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)专题15 数列不等式的证明 微点2 数学归纳法证明数列不等式(已下线)2023年北京高考数学真题变式题6-10
名校
3 . 1.已知等差数列
的前
项和为
,满足
,
,则下列结论正确的是( )
![](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/61764d97daa71e1fe31337c2e3811b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6ff9003520294adbe7eee1f2f972c9.png)
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2022-03-21更新
|
1052次组卷
|
10卷引用:浙江省金华市义乌市2020-2021学年高三上学期第一次模拟考试数学试题
浙江省金华市义乌市2020-2021学年高三上学期第一次模拟考试数学试题浙江省温州市瑞安中学2020-2021学年高三上学期1月测试数学试题(已下线)思想01 函数与方程思想 第三篇 思想方法篇(讲) 2021年高考二轮复习讲练测(浙江专用)(已下线)思想04 化归与转化思想 第三篇 思想方法篇(讲)-2021年高考二轮复习讲练测 (浙江专用)浙江省丽水市外国语实验学校2020-2021学年高三上学期期末数学试题浙江省金华第一中学2021-2022学年高一领军班下学期期中数学试题重庆市缙云教育联盟2020-2021学年高一上学期期末数学试题上海市普陀区2022届高三上学期11月调研测试(0.5模)数学试题(已下线)选择性必修第二册综合检测卷-2021-2022学年高二数学特色专题卷(人教A版2019选择性必修第二册)海南省琼海市嘉积中学2023-2024学年高二下学期期中数学试题(B卷)
4 . 如图,已知曲线
及曲线
.从
上的点
作直线平行于
轴,交曲线
于点
,再从点
作直线平行于
轴,交曲线
于点
.点
的横坐标构成数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f00a8f26afb72624ccd725c5067bdb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/dab59151-f4f0-41fd-a98e-3f310a3b07ba.png?resizew=222)
(Ⅰ)试求
与
之间的关系,并证明:
;
(Ⅱ)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af82160c02868bb45fc65d7597c84027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39da03b091bb40dd965458631bf50786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f51b9cac5b33e958d3fa9102fe29c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f00a8f26afb72624ccd725c5067bdb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/dab59151-f4f0-41fd-a98e-3f310a3b07ba.png?resizew=222)
(Ⅰ)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a00d0aaba11c21f851df46e3032e873.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825d463b3de2803d0dd66e44e2117454.png)
您最近一年使用:0次
解题方法
5 . 已知数列
满足:
,
.
(Ⅰ)证明:数列
为等比数列,并求数列
的通项公式;
(Ⅱ)记
,求使
成立的最大正整数n的值.(其中,符号
表示不超过x的最大整数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2438f2272d7b7ab51dbbe587025a553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5af8e317162f3c1bb3483b08207ea13.png)
(Ⅰ)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b484a6f707521fb604b8139753d2a6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeed2dd4e7c90200f05009bd071b3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
您最近一年使用:0次
2021-03-02更新
|
2042次组卷
|
7卷引用:浙江省名校协作体2021届高三下学期联考数学试题
浙江省名校协作体2021届高三下学期联考数学试题(已下线)专题20 数列综合-2020年高考数学母题题源全揭秘(浙江专版)(已下线)【新东方】高中数学20210429—010【2021】【高三下】(已下线)精做02 数列-备战2021年高考数学(文)大题精做(已下线)精做02 数列-备战2021年高考数学(理)大题精做(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)(已下线)第17节 等比数列及前n项和
解题方法
6 . 已知数列
的前
项和为
,且满足
,当
时,
.
(Ⅰ)证明
为等差数列,并求数列
的通项公式;
(Ⅱ)记数列
,记
为
前
项的积,证明:
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83ffedb600f7bebcf2f072dbb95e122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7ae2cdce39d8ecb11fda2306edf688.png)
(Ⅰ)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2617bb1f8a9a091ce2c35872295e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdf3ca29ac37bffc3f59cd4be5f62c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/bbc87a8eb0b2a1ff8eb65b75f02e3538.png)
您最近一年使用:0次
7 . 已知等差数列
满足
,
,
,
成等比数列;数列
满足
,
.
(1)求数列
,
的通项公式.
(2)数列
的前n项和为
,证明
.
![](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/7d93c1ae7b22099a5d4c1c4241e5ca18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0414c0b6fda7fee5eb71976e09da80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](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/cb27cc29c836ab7b82ad4a3acde8a3f5.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
2021-01-14更新
|
636次组卷
|
3卷引用:浙江省五湖联盟2020-2021学年高三上学期模拟考数学试题
8 . 已知
,
,
,
,
,记
为数列
的前
项和.
(1)求数列
,
的通项公式;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcba622ae8d5e614f5f59982ce9b9b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494852b4d9a733c2280ffdcc61922e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad9dba73c9dfa896e44bc19571f3377.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce54c7170eab13667a4423c52bf4896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe3ba11518192813958acdffb0b236f.png)
您最近一年使用:0次
19-20高一·浙江·期末
解题方法
9 . 已知数列
的前
项和为
,且
,
,数列
满足
,
.
(1)求数列
、
的通项公式;
(2)若数列
满足
且
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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/507d36a2c78c9bd0bb8ac860532825ba.png)
![](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/cb27cc29c836ab7b82ad4a3acde8a3f5.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731f88a91200a7e34af703b165fdb6c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dff70b911b566eee712f93b4570832a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
10 . 已知
为公差不为
的等差数列,
是等比数列
的前
项和,若
是
和
的等比中项,
,
.
(1)求
及
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb88d8831173a3319d95c502110ab31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c340fdadffa2f9120a70430ce477f8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e30678cd4f299ef67b719f13bfa863a.png)
您最近一年使用:0次