名校
解题方法
1 . 已知数列
的前
项和为
,若存在常数
,使得
对任意
都成立,则称数列
具有性质
.
(1)若数列
为等差数列,且
,求证:数列
具有性质
;
(2)设数列
的各项均为正数,且
具有性质
.
①若数列
是公比为
的等比数列,且
,求
的值;
②求
的最小值.
![](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/fc983f1bad03411ae64d84ff7bdf2551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a548095fa134cb2b52721af225cbbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193a0efaa1aa835eb3e061bb25dad4dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7470297de40027847c5c73fc5d1719c.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
①若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4338dd5d6ac02dbb9d5069eb98f436d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
7日内更新
|
250次组卷
|
4卷引用: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
江西省临川第二中学2023-2024学年高二下学期6月月考数学试题河南师范大学附属中学2024届高三下学期最后一卷数学试题江苏省泰州市2024届高三下学期四模数学试题(已下线)高二下期末考前押题卷01--高二期末考点大串讲(人教B版2019选择性必修)
名校
2 . 若数列
满足
,从数列
中任取2项相加,把所有和的不同值按照从小到大排成一列,称为数列
的和数列,记作数列
.
(1)已知等差数列
的前n项和为
,且
.
①若
,
,求
的通项公式,并写出
的前5项;
②若
,
,求数列
的前50项的和;
(2)若
,证明:对任意
或
,
,并求数列
的所有项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
(1)已知等差数列
![](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/a1a5945ce5c2114af8c18718ca8dc899.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58365ff21052f2f978c11844b002b933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb3fdeeb4afe6485ffb00bf83023e704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751859e4f0b1cb2c94fd5cca373de9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a50c3a2b8abc17a7e110f9811296a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559497cb5b10c9c489ee0cdc11fa2a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12329f3ac81209a815f8c4fa12c4b6cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d149f4ed2b72f3e3ee850e163ba35473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e23ba0aeb43a20799d1f414650203ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
您最近一年使用:0次
2024-04-30更新
|
113次组卷
|
3卷引用:江西省抚州市金溪县第一中学等校2023-2024学年高二下学期期中考试数学试卷
3 . 已知双曲线
,点
,经过点M的直线交双曲线C于不同的两点A、B,过点A,B分别作双曲线C的切线,两切线交于点E.(二次曲线
在曲线上某点
处的切线方程为
)
(1)求证:点E恒在一条定直线L上;
(2)若两直线与L交于点N,
,求
的值;
(3)若点A、B都在双曲线C的右支上,过点A、B分别做直线L的垂线,垂足分别为P、Q,记
,
,
的面积分别为
,问:是否存在常数m,使得
?若存在,求出m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017262e45089093f70001cae2c60257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363598fd39f2269952dc6ddd1201346c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16f528223f178103c2d8193b45e07af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7444e40f6ef2b62a680fb325a266cb63.png)
(1)求证:点E恒在一条定直线L上;
(2)若两直线与L交于点N,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9619a20d8dfa7aeaefd5fc1b76b5a40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)若点A、B都在双曲线C的右支上,过点A、B分别做直线L的垂线,垂足分别为P、Q,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2b58424e893df4e01c912f87e09095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf173f2377cc32d2a33d889729a224e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1f167ece5d18225840af97b39af9e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a22e8a68eb538caf433c0a280f6623.png)
您最近一年使用:0次
2024-02-05更新
|
1212次组卷
|
2卷引用:江西省抚州市临川第一中学2024届高三“九省联考”考后适应性测试数学试题(一)
名校
解题方法
4 . 若各项为正的无穷数列
满足:对于
,
,其中
为非零常数,则称数列
为
数列.记
.
(1)判断无穷数列
和
是否是
数列,并说明理由;
(2)若
是
数列,证明:数列
中存在小于1的项;
(3)若
是
数列,证明:存在正整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/782fdf6345302a3d8814acf96f6b3acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
(1)判断无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93068e5f0dedec981ec828ffa4458c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446e8a7985d4d3dd95c70dc4aad67861.png)
您最近一年使用:0次
2024-01-04更新
|
1522次组卷
|
3卷引用:江西省抚州市临川第一中学2024届高三“九省联考”考后适应性测试数学试题(一)
解题方法
5 . 定义:若将函数
的图象平移可以得到函数
的图象,则称函数
,
互为“平行函数”.已知
,
互为“平行函数”.
(1)判断并证明函数
的单调性;
(2)求实数a的值;
(3)求由函数
的图象、函数
的图象及y轴围成的封闭图形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c34d64a7bea0629324b9105d94556ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b8100c54a46bb7f8ba778307d7b03d.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求实数a的值;
(3)求由函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a5ff72ba4e9d01ecf0c0fe07a48058.png)
您最近一年使用:0次
6 . 无字证明来源于《几何原本》卷2的几何代数法(以几何方法研究代数问题),通过这一原理,很多的代数的公理或定理都能够通过图形实现证明.现有如图所示
,其中
、
为
边上异于端点的两点,
,
,且
是边长为
的正三角形,则下列不等式一定成立的是( )
![](https://img.xkw.com/dksih/QBM/2021/5/28/2730657997660160/2732120371486720/STEM/621fc4e6-3dce-4375-a13c-06dab1195f8d.png?resizew=244)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9001f0c06cf2c8f893a38b1dabe6219e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62e0d7822af5b4dc4ae1920d8c906e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://img.xkw.com/dksih/QBM/2021/5/28/2730657997660160/2732120371486720/STEM/621fc4e6-3dce-4375-a13c-06dab1195f8d.png?resizew=244)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2021-05-30更新
|
277次组卷
|
2卷引用:江西省临川一中暨临川一中实验学校2021届高三高考模拟押题预测卷数学(文)试题
7 . 勾股定理是一个基本的几何定理,中国《周髀算经》记载了勾股定理的公式与证明.相传是在商代由商高发现,故又有称之为商高定理.我国古代称短直角边为“勾”,长直角边为“股”,斜边为“弦”.西方文献中一直把勾股定理称作毕达哥拉斯定理.毕达哥拉斯学派研究了勾为奇数、弦与股长相差为1的勾股数:如3,4,5;5,12,13;7,24,25;9,40,41;……,如设勾为
(
),则弦为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2def5aa62f497709e1bd8258583d62fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e32b1201f042e9ad5b2c709d9b40e275.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-04-29更新
|
543次组卷
|
5卷引用:江西省临川第一中学暨临川一中实验学校2021届高三三模数学(理)试题
江西省临川第一中学暨临川一中实验学校2021届高三三模数学(理)试题慕华优策联考2021届高三第三次联考文科数学试卷慕华优策联考2021届高三第三次联考理科数学试卷(已下线)第2章 章末复习课(重点练)-2020-2021学年高二数学(文)十分钟同步课堂专练(人教A版选修1-2)(已下线)专题10 推理与证明小题大做-备战2022年高考数学冲刺横向强化精练精讲