1 . 已知数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)设
,且数列
的前
项和为
,若
都有不等式
恒成立,求
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/ae7436394b1aa194efb2dc97a953cbd9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.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/71b78297a65e7fad69635b19928ecc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f75ba8bc900ffb8d12a0923f7aa8285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-03-26更新
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1369次组卷
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5卷引用:福建省南平市2023-2024学年高二上学期期末数学试题
福建省南平市2023-2024学年高二上学期期末数学试题黑龙江省实验中学2023-2024学年高二下学期4月考数学试题(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)(已下线)专题03数列期末7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(人教B版2019选择性必修第三册)江西省临川第二中学2023-2024学年高二下学期6月月考数学试题
2 . 已知数列
的前n项和
满足
.
(1)求
的通项公式;
(2)设数列
满足
,记
的前n项和为
,若存在
使得
成立,求
的取值范围.
![](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/83fd67e206753eff52406291c19daa38.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6179eef1ce15617273d2c6b63bcfc1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45a31ac6e4efa09d5df5fb5818b6511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2022-11-20更新
|
928次组卷
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7卷引用:福建省南平市浦城县第三中学2023届高三上学期期中测试数学模拟卷试题(1)
福建省南平市浦城县第三中学2023届高三上学期期中测试数学模拟卷试题(1)中学生标椎学术能力诊断性测试2022-2023学高三上学期11月测试理科数学试题中学生标准学术能力诊断性测试2022-2023学高三上学期(新课改版)数学试题江苏省淮安市涟水县第一中学2022-2023学年高二上学期第二次阶段检测数学试题江苏省镇江市扬中市第二高级中学2022-2023学年高二上学期期末考前热身数学试题(已下线)拓展三:数列与不等式 -【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)陕西省西安铁一中学2023-2024学年高二上学期期末考试数学试题
名校
解题方法
3 . 已知数列
是等差数列,
是等比数列,且
,
,
,
.
(1)求数列
、
的通项公式;
(2)设
,数列
的前
项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e96fafcc7b7f783d436f853449208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b7b8f45c4af23b598b1bfee01db679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe0f4e8a80a2840c0f6929a8a6351b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc467423678b6bf191a1acf8e146082.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb682d8abea00bbeb778fd730fd98b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2022-06-02更新
|
1267次组卷
|
4卷引用:福建省南平第一中学2023-2024学年高二上学期第三次月考数学试卷
4 . 在数列
中,
,
.
(1)求证数列
为等差数列,并求出数列
的通项公式;
(2)若
,求数列
的前
项和
.
![](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/7d6098b279f2b3505505cb2e5862282d.png)
(1)求证数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b78e4a03d4595f14be42054b61dfc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/022e55604bc18f62502221660211433e.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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2021-11-28更新
|
1008次组卷
|
2卷引用:福建省南平市高级中学2022届高三上学期第三次月考数学试题
名校
解题方法
5 . 已知数列
的前
项和为
,且
,数列
的前
项积为
,且
.
(1)求
,
的通项公式;
(2)求数列
的前
项和
.
![](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/4300dca231e2f4b37f70900b33439d5e.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/f76b7b9f5e07607d763d9f6e419a1cf2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4bdc2a6d4fc387dc621f0b5a268c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
您最近一年使用:0次
2021-10-09更新
|
1399次组卷
|
10卷引用:福建省南平市2022届高三联考数学试题
解题方法
6 . 设数列
的前n项和为
,
为等比数列,且
,
.
(1)求数列
,
的通项公式;
(2)设
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4300dca231e2f4b37f70900b33439d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe0f4e8a80a2840c0f6929a8a6351b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57340a42514c3fbe082862151a9f1aca.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9221c0c92a526f65533cdc5400767af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2021-08-25更新
|
198次组卷
|
2卷引用:福建省南平市浦城县2020届高三上学期期中测试数学(文)试题
7 . 已知数列
中,
且
且
).
(1)证明:数列
为等差数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6065aaa8f3f103d1bc960da8318ce35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58894a01f8ad1b4e046737e8f61c041b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5157fd27806145d29683b9c6983d24.png)
(2)求数列
![](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)
您最近一年使用:0次
2021-01-17更新
|
1429次组卷
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4卷引用:福建省南平市邵武市邵武一中2023-2024学年高三上学期10月月考数学试题
8 . 已知数列
和
满足
,
,即数列
的前n项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434f451cbc6a57287ddb0cedd6869194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dc72a562d0fa6b380d16cdcf1cb14f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4bdc2a6d4fc387dc621f0b5a268c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
您最近一年使用:0次
9 . 已知数列
的前
项和为
.
(1)求数列
的通项公式
;
(2)令
,求数列
的前
项和
;
(3)令
,问是否存在正整数
使得
成等差数列?若存在,求出
的值,若不存在,请说明理由.
![](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/dcc8f3e6ffd1d667e4ff506915ad4a54.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8182f57c43fd1d8fb13161224687c469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b243344f9a3a769e257a0765c9fffc8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d55b8f37dfb7a3775d2f8268552c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed2a76df6f7e5f3e0ea3fddce4a0067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee956329e95a172d86c86b2f6af7aec.png)
您最近一年使用:0次
2018-07-13更新
|
1626次组卷
|
2卷引用:【全国市级联考】福建省南平市2017-2018学年高一下学期期末质量检测数学试题
10 . 设
为数列
的前
项和,已知
,
,
.
(1)求证:
是等差数列;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e30b49c411194a17a11b345c162b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853eace02560e7f1490694276c29a856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72d6f53ee1910be2f766d1dd71ec54b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c477d5bbc234f73de16724e4b35f0c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e7b3ef01c52c2b1dd9593edd2beea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2018-05-07更新
|
1096次组卷
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2卷引用:【全国市级联考】福建省南平市2018届高三第二次(5月)综合质量检查数学理试题