解题方法
1 . 已知数列
的前
项和
.
(1)求证:
是等差数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56c60f23e6ab26477288a9c7803070d0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91adba8efbf964e9e35547b0fd0ea36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
2 . 已知数列
的前
项和为
,且
为等差数列.
(1)证明:
为等差数列;
(2)若
,数列
满足
,且
,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/d3768db0f2e2881b810d44ddc39ff295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dfe5b322577f02fd19caab8cf20170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a8d7ec3afb812286ad33dd69d80c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c24437f62e6fab6d8baf7060f5c8ddd.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)
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3 . 已知数列
满足
,
.
(1)证明:
是等差数列;
(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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3953790a3764ec2a33ad3d17ba2e05.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416f4e43b21e0966b8d94292767b3bfd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971b88ebd254bd5e19b992c5e9244dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
解题方法
4 . 已知数列
满足
,
.
(1)证明
为等差数列,并求
的通项公式;
(2)若不等式
对于任意
都成立,求正数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f9ca737b137a45f33a4cd1d25713c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6657913ced8d5c98e9b2cfdeb3b965e8.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16388d3b944d3a5c131c584ef3913ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0d918963433c72a174ece368352cd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-10-30更新
|
931次组卷
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5卷引用:河南省周口市项城市第一高级中学2023-2024学年高三上学期第四次段考数学试题
名校
解题方法
5 . 已知数列
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aedfa8f30e122365dfa1d875a9a2a22.png)
(1)证明:数列
是等差数列,并求数列
的通项公式;
(2)设
,数列
的前
项和为
,若
恒成立,试求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aedfa8f30e122365dfa1d875a9a2a22.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf3da897eb73b729f66bb0d700775c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ad738dc3a9c27a05fbb0eb65d403d9.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/24e2229881f9d119f44e64e6c0164458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2023-05-13更新
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1557次组卷
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4卷引用:河南省商丘市睢阳区商丘市第一高级中学2023-2024学年高三上学期期中数学试题
河南省商丘市睢阳区商丘市第一高级中学2023-2024学年高三上学期期中数学试题河南省信阳市2023-2024学年高三第一次教学质量检测数学试题东北三省四市教研联合体2023届高三二模数学试题(已下线)专题11 数列前n项和的求法 微点4 裂项相消法求和(二)
6 . 记
为正项数列
的前n项和,已知
,
.
(1)求数列
的前n项和
;
(2)若
,求数列
的前n项和
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a1a8de0e65f260670fd538890b8e55.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b20224f6ba644d885435646a9b91b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2023-03-25更新
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1105次组卷
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5卷引用:河南省濮阳市第一高级中学2022-2023学年高二下学期期中数学试题
名校
解题方法
7 . 数列
中,
,
(
为正整数),则
( )
![](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/588e4f939835eeb5feefdb5d37c921e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-02-08更新
|
1023次组卷
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5卷引用:河南省实验中学2022-2023学年高二下学期期中数学试题
河南省实验中学2022-2023学年高二下学期期中数学试题湖南省长沙市师大附中梅溪湖中学(湖南师大附中梅溪湖中学)等2校2023届高三下学期3月联考数学试题(已下线)模块四专题1重组综合练(河南)高二沪教版(2020) 选修第一册 高效课堂 第四章 4.3 数列(已下线)1.2.1 等差数列的概念及其通项公式8种常见考法归类(1)
8 . 已知数列
满足
.
(1)证明:数列
是等差数列;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f00ce8722a49f404e1dca6d2ed89dc.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0b53ddd01ed8617540f85ce89ce82d.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6a0d136f2be8c63f966d4da3392ba.png)
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2022-12-06更新
|
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7卷引用:河南省濮阳市2022-2023学年高二上学期期中数学试题
河南省濮阳市2022-2023学年高二上学期期中数学试题河南省青桐鸣2023届高二上学期11月联考数学试题河南省周口市项城市正泰博文学校等3校2022-2023学年高二上学期11月月考数学试题安徽省六安第一中学2022-2023学年高二上学期期末数学试题(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)(已下线)专题15 数列不等式的证明 微点6 数列不等式的证明综合训练安徽省阜阳市第三中学2023-2024学年高二上学期一调考试(10月月考)数学试题
名校
解题方法
9 . 数列
中,
为
的前
项和,
,
.
(1)求证: 数列
是等差数列,并求出其通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/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/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e1d65c1a1218c3debb4604fbb97ed7.png)
(1)求证: 数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ee300c6184e79e9f55bfac27ac73cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2022-11-04更新
|
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2卷引用:河南省南阳市2022-2023学年高三上学期期中数学理科试题
10 . 在数列
中,
,
,且
.
表示不超过x的最大整数,若
,数列
的前n项和为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58424966071e1494337f714168a769f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2140baafc3802f7e5a6b31f8e5de5d06.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/bd33ffdddd0b530062f8c0eedbb91cfa.png)
A.2 | B.3 | C.2022 | D.2023 |
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