名校
解题方法
1 . 设
是各项都为正的单调递增数列,已知
,且
满足关系式:
,
.
(1)求数列
的通项公式;
(2)令
,求数列
的前n项积
.
![](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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d744939dcdb1187d40f256d4934f440b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af54f5452111f6b078d40ab756416e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2 . 已知数列
的前n项和为
,
,数列
满足
,且
均为正整数.
(1)是否存在数列
,使得
是等差数列?若存在,求此时的
;若不存在,说明理由;
(2)若
,求
的通项公式.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec893189bd1985e1c079c0e7e6afaa71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55e03428497ac0ea2aa80fe5bdcd939.png)
(1)是否存在数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bc4389ba9a9359655156924a35a3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
3 . 在等差数列
中,已知
成等差数列.
(1)求数列
的通项公式;
(2)数列
是否为等比数列?若是求其前
项和,若不是,请说明理由;
(3)设
,且
,求
的所有取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52c7ae4c82590ee0bb8a30b41d21230.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4844ada5b5eb39d704345bb4e6080d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9812262de14506c8ade975ca8f19017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084b7d72097a2a79ea3a019a0fdd14bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
您最近一年使用:0次
2024-04-12更新
|
480次组卷
|
2卷引用:河南省TOP二十名校2024届高三下学期4月冲刺一数学试卷
4 . 已知数列
是等比数列,
,
,
,
成等差数列.
(1)求
的通项公式和
;
(2)数列
满足
;当
时,
;当
时,
.记数列
的前
项和为
.
①若
,求
的值;
②若
,求证:
.
![](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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d473bfcc52ebc119430335531488a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8822db269777fddd605b50521576b57.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5adec817865eefb615fb692c4b7f473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f536ba19aa3c3b1be97b33dfd852f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f205eb08ae9ffe22dc6fbfe2b1fe65fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b434cd915f3e6fbc3028f86f358332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3054785bacfe0537831c337f57ab92.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)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b54a7884388655cea734328f3e43f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59268f6dd353af2dedd8269a2bc5b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0f924858fdfc9403142fcbce46de32.png)
您最近一年使用:0次
名校
解题方法
5 . 已知数列
满足
,数列
首项为2,且满足
.
(1)求
和
的通项公式
(2)记集合
,若集合
的元素个数为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9773e0e15fd4d50ed88b1edc6b5922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c68a4dc8539ad135d9c46adb013194.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210e8c674bf9278f5baae91cb2e13167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-01-02更新
|
571次组卷
|
2卷引用:四川省绵阳市南山中学实验学校2024届高考补习年级二诊模拟数学试题(四)
6 . 已知空间向量列
,如果对于任意的正整数
,均有
,则称此空间向量列
为“等差向量列”,
称为“公差向量”;空间向量列
,如果
且对于任意的正整数
,均有
,
,则称此空间向量列
为“等比向量列”,常数
称为“公比”.
(1)若
是“等比向量列”,
为单位向量,求
(用
表示);
(2)若
是“等差向量列”,“公差向量”
,
,
;
是“等比向量列”,“公比”
,
,
.求
.
(3)若
是“等差向量列”,
,记
,
且
,等式
对于
和2均成立,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4f79c1b52b08b72cf398a8e62e5fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1625356f589bccd60dabbd6f3dfad5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4f79c1b52b08b72cf398a8e62e5fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337ab4dc61186ca58bb0605cb6d02df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579cbe6b08d6d7f4421ff8a78a6e2c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da12988ddfd0d6226744004d7437aecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94cff7e7655e703528f2b1346420d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3ac83c571110d41a396d12d8eea1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5faa496b58c0a03ea741e2d8b2f821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5faa496b58c0a03ea741e2d8b2f821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b152d9afeb54bae45a111b5ffa34cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3c66f190f2758eef96ad39f64e88ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4f79c1b52b08b72cf398a8e62e5fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727582a95b94565368249c38599f6705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd701bb4b32bdffa38d8ad232f63fc49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf8f9249000f1bd456c451455add663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5faa496b58c0a03ea741e2d8b2f821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b01c2083c7a345df61859f1c953305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6423b222ad6987817ac8d2f8185760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a5c8d7c03130b5630121835b29ce29.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4f79c1b52b08b72cf398a8e62e5fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd701bb4b32bdffa38d8ad232f63fc49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62e08b73465d312e406836eb58c8a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5dd1562138ab60802c33a17a8d7867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c549a4c7303ca973cd890eb38a071a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ea0e903fbb4c8ce04133b9969578c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8ae422c68cbaf553dd1afecd4723eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
7 . 记
为数列
的前n项和,已知
,
,数列
满足:
,且
.
(1)求数列
的通项公式;
(2)令
,求数列
的前n项和
的最值.
![](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/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911c88654ea7669c5e54542b0f16d89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50a454957acee6310d508674aa8b300.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef0cb445c3cd097581c35e2b40750a0.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
2023-11-07更新
|
2001次组卷
|
2卷引用:河南省湘豫名校联考2023-2024学年高三上学期一轮复习诊断考试(二)数学试题
8 . 已知数列
的各项均为非负实数,且对任意正整数
,均有
.
(1)若
成等差数列,证明:存在无穷多个正整数
,使得
;
(2)若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/336407650f4fc2bdfdbe639c03ebb599.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea867f78d52b7382c38e8fc6e2e2a9c0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c2570afdfeebd6bfbcc6da5edc878f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce88126c3cbc88e03d38f56b7da315b6.png)
您最近一年使用:0次
解题方法
9 . 记
为数列
的前
项和,已知
,
.
(1)求
的通项公式;
(2)令
,证明:
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6b7eeda1ca25d1630e3eca48061c7d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053d545d85e8e4b7f96e41500efd6945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3593087fb880597ad563d015c7027ca.png)
您最近一年使用:0次
解题方法
10 . 已知数列
满足
,
.
(1)求
的值;
(2)求数列
的通项公式
;
(3)若数列
满足
,
.对任意的正整数
,是否都存在正整数
,使得
?若存在,请给予证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89a1ece7b4658e82db0d01a2903b75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a868c6384a7740c4fc59c30f99a8a1d6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeabbc1dd7447cddfc6689535fbb61ec.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0936ddc154297c06d5bcdb5c156db68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5e1c2a3adbf590f0fc85e2142cae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c8947e097f55291a62e2930dd595ac.png)
您最近一年使用:0次
2023-07-09更新
|
484次组卷
|
3卷引用:北京市东城区2022-2023学年高二下学期期末统一检测数学试题
北京市东城区2022-2023学年高二下学期期末统一检测数学试题【北京专用】专题01数列(第一部分)-高二上学期名校期末好题汇编(已下线)专题02 等比数列4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(北京专用)