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1 . 已知数列
满足
,
,
数列
,
的前n项和分别为.
(1)求
,并证明数列
为等比数列;
(2)当
时,有恒成立,求正整数m的最小值.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b13a6e1d671215fc96e4bee3541d1096.png)
![](/uploads/image/squformula/60d3eaf50c4cacfbe369e12984e8b31a.png)
![](/uploads/image/squformula/a784243ca60ed9fa55480c6987d40605.png)
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(1)求
![](/uploads/image/squformula/d7de777f1b9ad8ffaf3568c093b2f7c5.png)
![](/uploads/image/squformula/c8194a62bc60a9da9b5cf76f9dc0fa09.png)
(2)当
![](/uploads/image/squformula/856b137a34d2d5b20671b7a3c7a29606.png)
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2 . (1)在等比数列
中,已知,求;
(2)一个等比数列的首项是
,项数是偶数,其奇数项的和为
,偶数项的和为
,求此数列的公比和项数.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)一个等比数列的首项是
![](/uploads/image/squformula/bdaa19de263700a15fcf213d64a8cd57.png)
![](/uploads/image/squformula/83fd1dadbe1b2cafc0cf8b5bb8b18ed9.png)
![](/uploads/image/squformula/5ca15cd772284da8cf1899d388df3a8c.png)
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1卷引用:第四章 数列(知识归纳 题型突破)-2023-2024学年高二数学单元速记·巧练(苏教版2019选择性必修第一册)
(已下线)第四章 数列(知识归纳 题型突破)-2023-2024学年高二数学单元速记·巧练(苏教版2019选择性必修第一册)
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解题方法
3 . 在等比数列
中.
(1)已知
,
,求前4项和
;
(2)已知公比
,前6项和
,求.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知
![](/uploads/image/squformula/2815b24f5a89be7ae53aed93182e8988.png)
![](/uploads/image/squformula/ea432be66a5d2f9c5198ff656b18fd32.png)
![](/uploads/image/squformula/0f30f56664446f32dbbc2c5f12a99374.png)
(2)已知公比
![](/uploads/image/squformula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](/uploads/image/squformula/a8b7b67a73a815fb9792f0567396a78b.png)
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1卷引用:广西壮族自治区三新学术联盟2023-2024学年高二上学期期末教学质量检测数学试题
解题方法
4 . 已知数列
满足:
,
.
(1)求证:数列
为等差数列;
(2)设
,求数列
的前
项和
;
(3)设
,求数列
的前
项和
.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](/uploads/image/squformula/7b8fcc79d25afc6cedc04f020d425abc.png)
(1)求证:数列
![](/uploads/image/squformula/41cf1da18d91f7c98086553d157d1a87.png)
(2)设
![](/uploads/image/squformula/ef4cecbdebeb5d12fbe1d54b81cc05a8.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)设
![](/uploads/image/squformula/03d1e0b86b68d7ad69dae1d5bdbbccff.png)
![](/uploads/image/squformula/57ef6d44448092ebdb9e4a49d866a749.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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智能选题,一键自动生成优质试卷~
5 . 已知数列
是等差数列,满足
,
,数列
是首项为1的等比数列,且
,
,
成等差数列.
(1)求
,
的通项公式;
(2)设
,求数列
的前
项和.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/be0d1a492ec22f4ca2372e2c59c61d6c.png)
![](/uploads/image/squformula/79b50b3927041221a53f19b6a0549d71.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/d0eeacc31bfbd4c536bb52bbaec43dd3.png)
![](/uploads/image/squformula/1a8aada7b854c906305d0747c33f9929.png)
![](/uploads/image/squformula/57483e04fd1840c87ac5325157149877.png)
(1)求
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](/uploads/image/squformula/1d44ddab6e0c60119be69985ae7fa65b.png)
![](/uploads/image/squformula/57ef6d44448092ebdb9e4a49d866a749.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
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6 . 数列
的前
项和为
,
,则![](/uploads/image/squformula/e3f7fda69e2b32b9ced2239f915fa59b.png)
_________ ;设数列
的前
项和为
,则![](/uploads/image/squformula/7978d7bd6f6caf9ac9837ffce5f89654.png)
________ .
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/a742ea39d5f4c69ecb789537648bcb4b.png)
![](/uploads/image/squformula/e3f7fda69e2b32b9ced2239f915fa59b.png)
![](/uploads/image/squformula/362832fa3d3c13c1eafd565349d66dce.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](/uploads/image/squformula/7978d7bd6f6caf9ac9837ffce5f89654.png)
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解题方法
7 . 已知数列
的前
项和为
,且
为定值.
(1)求
的通项公式;
(2)求数列
的前
项和
.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/ae734ad099abbb2f7efe7d7a6a4169fd.png)
![](/uploads/image/squformula/d2f92296e96b4552e38adee06620ce02.png)
(1)求
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](/uploads/image/squformula/c1b71c0f98136b16dbea8f7b5faab298.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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8 . 有理数都能表示成
(
,
,且
,
与
互质)的形式,于是有理数集可表示为
.任何有理数
都可以化为有限小数或无限循环小数.反之,任一有限小数也可以化为
的形式,从而它是有理数.对于无限循环小数
,它可以表示成
,这是数列
的无穷项和,记为
.设该数列的前
项和为
,经计算得
,当
趋于无穷大时,
趋于0,则
,即可得
.
(1)数列
的无穷项和是有限小数吗?请说明理由;
(2)
是有理数吗?请说明理由.
![](/uploads/image/squformula/a0be44077d42cfffece905b1af13e000.png)
![](/uploads/image/squformula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](/uploads/image/squformula/00cb345f4f5412cc958e4f2085e8f571.png)
![](/uploads/image/squformula/59b2400d72b1e3145cb21ba719d8a968.png)
![](/uploads/image/squformula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/230e0a440b8889447f016ae8e3ab6177.png)
![](/uploads/image/squformula/a0be44077d42cfffece905b1af13e000.png)
![](/uploads/image/squformula/a0be44077d42cfffece905b1af13e000.png)
![](/uploads/image/squformula/83b4464ed7fbac5ee80445dfdeb21c98.png)
![](/uploads/image/squformula/3a2b130c67213517e483f1286988414b.png)
![](/uploads/image/squformula/6dc4a96a7601995efe5b7891966cdb45.png)
![](/uploads/image/squformula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/de4da73ba2be55c716b1104cae2ceeb9.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/bd56eb9d6ca68d288c232e59847ddf63.png)
![](/uploads/image/squformula/43a52efd70c382a8322f7dede588fa66.png)
![](/uploads/image/squformula/9cc8ff3a0d73bf02f4bb5163f730b203.png)
(1)数列
![](/uploads/image/squformula/8c3b9101b74e00ffcba4a99e40a8e521.png)
(2)
![](/uploads/image/squformula/a2b0d5cf741c9fe8a0cfcf6cdbcd90ce.png)
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1卷引用:山西省长治市2023-2024学年高二上学期1月期末数学试题
23-24高二上·全国·期末
解题方法
9 . 已知数列
,
满足
.
(1)证明: 数列
为等比数列;
(2)令
,求数列
的前n项和
.
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/034ba25825c13725931c483aa47c9363.png)
![](/uploads/image/squformula/1f8e283499f5b1e66f009b5aab12a2a1.png)
(1)证明: 数列
![](/uploads/image/squformula/5344eadd4711db34e3f935aedd5fb270.png)
(2)令
![](/uploads/image/squformula/943ed820507a5e5d6ac1b1e46be53535.png)
![](/uploads/image/squformula/57ef6d44448092ebdb9e4a49d866a749.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
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1卷引用:高二上学期期末数学模拟试卷(人教a版2019选择性必修第一册 第二册)-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教a版2019)
(已下线)高二上学期期末数学模拟试卷(人教a版2019选择性必修第一册 第二册)-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教a版2019)
2023高二上·江苏·专题练习
解题方法
10 . 已知等比数列
的各项均为正数,其前n项和为
,若 ,则![](/uploads/image/squformula/614306cc3f34bdee4d5d885b79667645.png)
____ .
![](/uploads/image/squformula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](/uploads/image/squformula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](/uploads/image/squformula/614306cc3f34bdee4d5d885b79667645.png)
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1卷引用:4.3.3 等比数列的前n项和(6大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)
(已下线)4.3.3 等比数列的前n项和(6大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)
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