1 . 若某类数列
满足“
,且
”
,则称这个数列
为“
型数列”.
(1)若数列
满足
,求
的值并证明:数列
是“
型数列”;
(2)若数列
的各项均为正整数,且
为“
型数列”,记
,数列
为等比数列,公比
为正整数,当
不是“
型数列”时,
(i)求数列
的通项公式;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b781279c765cfbfb88b28bc5b6cfb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be613fff0421d9be9e8bb5eb8b07c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00cf22c8daa450289ffdce46b85024b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85726f99979d3793ea28b77a7708f4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07cefac60bb3fcde0bded804501c90b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(i)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15b6cf3d2cdd85baed3056ac375d3c.png)
您最近一年使用:0次
2 . 已知
是由正整数组成的无穷数列,该数列前
项的最大值记为
,即
;前
项的最小值记为
,即
,令
(
),并将数列
称为
的“生成数列”.
(1)若
,求其生成数列
的前
项和;
(2)设数列
的“生成数列”为
,求证:
;
(3)若
是等差数列,证明:存在正整数
,当
时,
,
,
,
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d7fcd7b8817a82478bd872bc61a132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09b082619df0e06d2dcd83a3bc0fb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd9b9869da85bfffac7c01d7c34e35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414f4f53b4ae5085836107278784e3ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7f82f00fe6163833431241820687ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef1643721ad2b804d4ee2ba1a091a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b6a226d310f16ea311db851216e894.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c29bfcb2e31e3c21967ede660eaa0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39222f0687c9124bddb35544bcc7798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
您最近一年使用:0次
2024-04-17更新
|
1606次组卷
|
10卷引用:广东省梅州市2024届高三下学期总复习质检(二模)数学试题
广东省梅州市2024届高三下学期总复习质检(二模)数学试题(已下线)模块五 专题4 全真能力模拟4(人教B版高二期中研习)(已下线)数学(广东专用02,新题型结构)(已下线)模块三 专题2 新定义专练【高二下人教B版】(已下线)5.2 等差数列和等比数列(高考真题素材之十年高考)(已下线)第4套 新高考全真模拟卷(二模重组)(已下线)压轴题05数列压轴题15题型汇总-1(已下线)第六套 艺体生新高考全真模拟 (二模重组卷)湖北省荆州市沙市中学2024届高三下学期高考全真模拟数学试卷广西南宁市第三十六中学2024届高三下学期适应性训练数学试题
2024高三·全国·专题练习
解题方法
3 . 设数列
的各项为互不相等的正整数,前
项和为
,称满足条件“对任意的
,
,均有
”的数列
为“好”数列.
(1)试分别判断数列
,
是否为“好”数列,其中
,
,
并给出证明;
(2)已知数列
为“好”数列,其前
项和为
.
①若
,求数列
的通项公式;
②若
,且对任意给定的正整数
,
,有
,
,
成等比数列,求证:
.
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8134cb1772cc78e318280a19fe4124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)试分别判断数列
![](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/677e46ecd051c92489c0d1d458932f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7bb72b3ebbca741b3eda49cd617c058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
(2)已知数列
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a90323142c0d14429c5124541a295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff2eb0fb845a82db057a3bbaf314c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb4a3b2465a8dcc8a677882c8d6862d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d4ad9afdd266c6d38421bdfccd45e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b924cf3c2252a73ec6809ca262643f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbdd68463267382ef3d410eb5417a23.png)
您最近一年使用:0次
名校
解题方法
4 . 已知数列
满足
,
,
,
成等差数列.
(1)求证:数列
是等比数列,并求出
的通项公式;
(2)记
的前n项和为
,证明:
.
![](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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479c0564241789f8f52ac4fda26e9904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6197e2365d7f39507f8671acfc25a339.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](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/ef130855c8dc1accbff28762858f20bf.png)
您最近一年使用:0次
2024-06-09更新
|
555次组卷
|
2卷引用:江西省赣州市2023-2024学年高三下学期5月适应性考试数学试题
5 . 已知数列
满足
,
,设
,其中
.
(1)求证:数列
是等差数列;
(2)求数列
的前
项和
;
(3)设数列
的前
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/c4cb570b2e190d3a0fc98dd2ec3a7dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb3133b7ca679c841508e1f9431ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c0b04ff1a24b233372000a40ff868a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19593d4d64894906920c3d10f3e2d9a6.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/3bb790434e3ddf0e34b72bf8f7634c7d.png)
您最近一年使用:0次
6 . 设自然数
,由
个不同正整数
构成集合
,若集合
的每一个非空子集所含元素的和构成新的集合
,记
为集合
元素的个数
(1)已知集合
,集合
,分别求解
.
(2)对于集合
,若
取得最大值,则称该集合
为“极异集合”
①求
的最大值(无需证明).
②已知集合
是极异集合,记
求证:数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23747e7321187323c665a641adb49e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84357e7e15c0b4187ea69a4d555ef171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29fd31a1808968790032a671f64be90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a84d5316c5db87fda9b7d615c9dce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29fd31a1808968790032a671f64be90.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ccaf946a034215b8c49c12a1aff7790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d160c80e7542650f9ac8ff3981548ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11391d21b5da91adc137d57a73c19b83.png)
(2)对于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84357e7e15c0b4187ea69a4d555ef171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a84d5316c5db87fda9b7d615c9dce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a84d5316c5db87fda9b7d615c9dce6.png)
②已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84357e7e15c0b4187ea69a4d555ef171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e9ca7e90d47d7ee295338bbac2d8d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7477e3d7c54f409ee9905e81c9cbe2f.png)
您最近一年使用:0次
名校
解题方法
7 . 在无穷数列
中,若对任意的
,都存在
,使得
,则称
为m阶等差数列.在正项无穷数列
中,若对任意的
,都存在
,使得
,则称
为m阶等比数列.
(1)若数列
为1阶等比数列,
,
,求
的通项公式及前n项的和;
(2)若数列
为m阶等差数列,求证:
为m阶等比数列;
(3)若数列
既是m阶等差数列,又是
阶等差数列,证明:
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd2c3166d0bfd9e64bdc85081445e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57ae28a9ca230ff60fff6406b06ba96.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/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd2c3166d0bfd9e64bdc85081445e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8483c0e1d0daabfa8130baa9737eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674f03ad5f8c00ce301ecb176fb23277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25fe433dbc540279bc50cf65c7f5fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec50a8616d7700de94ee53c2b5dac43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec50a8616d7700de94ee53c2b5dac43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2024-05-31更新
|
367次组卷
|
3卷引用:贵州省毕节市2024届高三第三次诊断性考试数学试题
名校
解题方法
8 . 设
,
.如果存在
使得
,那么就说
可被
整除(或
整除
),记做
且称
是
的倍数,
是
的约数(也可称为除数、因数).
不能被
整除就记做
.由整除的定义,不难得出整除的下面几条性质:①若
,
,则
;②
,
互质,若
,
,则
;③若
,则
,其中
.
(1)若数列
满足,
,其前
项和为
,证明:
;
(2)若
为奇数,求证:
能被
整除;
(3)对于整数
与
,
,求证:
可整除
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72ea8ec0d9f8b1cfc4de834b8bfb608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87803b7cee18366b89d51799250df510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6705dba65746e1d4cac6a268b3c806ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bda3d07c2fef4d6af4a13ade4c743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0601879ae4ca9592246d135bfa48658c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383eb235f8e0ceda13367b16d29e0180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503618b9bfb53a06f0ec6a5e427dcdbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0da20edf2714109dcfded7e212ec44a.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12059d1dac926a235ccd40c3b61b1b6.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/ed9dbd8ed61db4f1c14f6b0e5f071200.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1e4de97f8490fddcff16afe8583266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)对于整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b96cdd9e003120b6102d927dbf53e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5009ce2d56180d31204f77c871fb375c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b326965628b5d967aafe9e696fdc07.png)
您最近一年使用:0次
2024-05-19更新
|
545次组卷
|
2卷引用:山东中学联盟2024届高考考前热身押题数学试题
解题方法
9 . 如图所示数阵,第
行共有
个数,第m行的第1个数为
,第2个数为
,第
个数为
.规定:
.
(2)求证:每一行的所有数之和等于下一行的最后一个数;
(3)从第1行起,每一行最后一个数依次构成数列
,设数列
的前n项和为
是否存在正整数k,使得对任意正整数n,
恒成立?如存在,请求出k的最大值,如不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdd4f87e7e7e32d723d7e97d980db42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29a285201fd7e0ad70fa7431cb89a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0749c4129afc0c704155f522290b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae0b861522b18be1753acc4474cbc9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5222268dda9dcb9b660f3cbedbb37757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ef9ec4340eabb42722042c65cc60d8.png)
(2)求证:每一行的所有数之和等于下一行的最后一个数;
(3)从第1行起,每一行最后一个数依次构成数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e8660fb54ba32b037b392b75316087.png)
您最近一年使用:0次
2024-05-14更新
|
1008次组卷
|
2卷引用:江苏省苏锡常镇四市2024届高三教学情况调研(二)数学试题
名校
10 . 在正项无穷数列
中,若对任意的
,都存在
,使得
,则称
为
阶等比数列.在无穷数列
中,若对任意的
,都存在
,使得
,则称
为
阶等差数列.
(1)若
为1阶等比数列,
,求
的通项公式及前
项和;
(2)若
为
阶等比数列,求证:
为
阶等差数列;
(3)若
既是4阶等比数列,又是5阶等比数列,证明:
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7905fd422e78a1d22ff6f11950bc5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7f4b6e82924087d9fa4523cd509d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7905fd422e78a1d22ff6f11950bc5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a08caf919ff9fa62e20d91af57c401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0831836c71efc1b1ffdb73073da2a2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc71a2fd8c6b263feea5ff5d6a36121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2024-03-10更新
|
960次组卷
|
4卷引用:河南省TOP二十名校2024届高三下学期质检一数学试题