1 . 已知数列
满足
,其前
项和为
,设函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516f11b2cdd36ea3ae58cb80f4a53bb3.png)
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f60fda2a90778fe9c4bca7c9fdffefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc15991d3009d5a2963db9a6fbbe2f7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516f11b2cdd36ea3ae58cb80f4a53bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f739c616992463e5f1eb0e9579169d.png)
A.0 | B.1 | C.1012 | D.2024 |
您最近一年使用:0次
名校
解题方法
2 . 已知数列
的首项为1,设
,
.
(1)若
为常数列,求
的值;
(2)若
为公比为2的等比数列,求
的解析式;
(3)数列
能否成等差数列,使得
对一切
都成立?若能,求出数列
的通项公式,若不能,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba1e3a2077fc5506a2ff9c0e6b624ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356dcbfbfc0b929ea6204011ce8efd1d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee15cd0d7af69d66344896aeddd5403d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2023-09-10更新
|
469次组卷
|
3卷引用:江苏省兴化市2022-2023学年高二下学期期中数学试题
3 . 求和:
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4fbdf4e166ccbf00746741245a73cdd.png)
A.512 | B.1024 | C.5120 | D.10240 |
您最近一年使用:0次
4 . 给出定义:设
是函数
的导函数,
是函数
的导函数,若方程
有实数解
,则称(
)为函数
的“拐点”.经研究发现所有的三次函数.
都有“拐点”,且该“拐点”也是函数
的图像的对称中心,已知函数
(1)求出
的对称中心;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c553558c1640e17b0c67395627d488c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f087ded8039eedaa8aa724b81ec393e9.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88afe5c5be8dc12217ccbef588cc61c.png)
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5 . 已知数列
的项数为
,且
,则
的前n项和
为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818b2c2d51316638cf39039d6cb4d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098afe75dd67aa4c2d1f0b6616c4c1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8581c9f3ebeea3e48a5b5239705a0b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818b2c2d51316638cf39039d6cb4d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-04-27更新
|
970次组卷
|
4卷引用:江苏省南京市雨花台中学、金陵中学河西分校、宁海中学2022-2023学年高二下学期期中联考数学试题
6 . 函数
,数则
满足
.
(1)求证:
为定值,并求数列
的通项公式;
(2)记数列
的前n项和为
,数列
的前n项和为
,若
对
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c18038df6ffb04b228446e28449a422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397f04518d59979ccb2e97ca54d67355.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3caaf39cc15fc52ecae71ac5bc0e1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0d58a97a8cebc0ff57ed57b4a3ed84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5a1bddcf44de4a79760022930d5f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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7 . 对于三次函数
,给出定义:设
是函数
的导数,
是函数
的导数,若方程
有实数解
,则称
为函数
的“拐点”.某同学经过探究发现:任何一个三次函数都有“拐点”;任何一个三次函数都有对称中心,且“拐点”就是对称中心.若函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6bd00360c538fa23d145c38ca193a5e.png)
A.![]() |
B.函数![]() |
C.过点![]() ![]() |
D.当![]() ![]() |
您最近一年使用:0次
2023-03-11更新
|
1686次组卷
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12卷引用:福建省漳州市第五中学2022-2023年高二下学期期中考试数学试题
福建省漳州市第五中学2022-2023年高二下学期期中考试数学试题浙江省台州市八校联盟2022-2023学年高二下学期期中联考数学试题海南省儋州市第三中学2022-2023学年高二下学期期中考试数学试卷河北省邯郸市鸡泽县第一中学2022-2023学年高二下学期第一次月考数学试题山西省晋中市平遥县第二中学2022-2023学年高二下学期3月月考数学试题山东省威海市乳山市银滩高级中学2022-2023学年高二下学期4月月考数学试题(已下线)第五章 一元函数的导数及其应用(单元综合检测)-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第二册)黑龙江省大庆市肇州县第二中学2022-2023学年高二下学期4月月考数学试题福建省连城县第一中学2022-2023学年高二下学期5月月考数学试题山西省晋中市2023届二模数学试题(B卷)(已下线)专题07 导数(已下线)专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)
名校
8 . 已知
,利用课本中推导等差数列前
项和的公式的方法,可求得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e1cfb0e1c279333b24745521c9e7dc.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/581b756f5e114a2f8d98730af6a7087f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e1cfb0e1c279333b24745521c9e7dc.png)
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2023-03-02更新
|
1353次组卷
|
5卷引用:山东省淄博市沂源县沂源县第一中学2022-2023学年高二下学期期中数学试题
9 . 已知函数
满足
,若数列
满足
,则数列
的前16项的和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfca9e2cea383880fb2dfe0e71b9e2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c99cddaade01dd53a84b471c21311c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2023-02-22更新
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1501次组卷
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6卷引用:新疆生产建设兵团第二师八一中学2022-2023学年高二下学期期中考试数学试题
新疆生产建设兵团第二师八一中学2022-2023学年高二下学期期中考试数学试题江苏省常州市第一中学2022-2023学年高二上学期期末数学试题河南省新乡市第一中学2022-2023学年高二下学期3月月考数学试题(已下线)微专题1 数列综合应用-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)(已下线)第四节 数列求和 A素养养成卷(已下线)专题04数列求和的6种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
10 . 已知各项为正数的数列
的首项是1,满足:
,数列
的前
项项和是
.
(1)判断数列
单调性,并说明理由;
(2)求数列
的通项公式;
(3)
表示正整数
的各个数位上的数字之和,如
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7a4605f6cdcaabece521f8d2848b20.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)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bdc58f24200ee4e4ed62581ecc9450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cf385f1d2365e9ac40542df31f66f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b8fa53eb04b784845e2114ec2f6322.png)
您最近一年使用:0次
2023-01-02更新
|
401次组卷
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3卷引用:期中模拟预测卷03(测试范围:选修一+选修二)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
(已下线)期中模拟预测卷03(测试范围:选修一+选修二)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)上海市奉贤中学2021-2022学年高二下学期期中数学试题(已下线)重难点02数列求和的五种解题方法-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)