名校
解题方法
1 . 设数列
的前n项和为
,
,
是公差为1的等差数列.
(1)求
的通项公式;
(2)记
,解关于n的不等式
.
![](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/c5b0da4fcbf9ec484dd9444a18609065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832d1e3a06f59a35396aac6e12c5e2ee.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfbb16b9c05204eff7f0ad025c0c466.png)
您最近一年使用:0次
2 . 设关于
的不等式
的解集中整数的个数记为
.数列
的前
项和为
.
(Ⅰ)求数列
的通项公式;
(Ⅱ)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79af3c47fb122a688720cf3702bee86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.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/08eb71ecf8d733b6932f4680874dbbf3.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63059fbfd9548449b9d90cc22f7fea00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
解题方法
3 . 同余定理是数论中的重要内容.同余的定义为:设
且
.若
,则称a与b关于模m同余,记作
(“|”为整除符号).
(1)解同余方程:
;
(2)设(1)中方程的所有正根构成数列
,其中
.
①若
,数列
的前n项和为
,求
;
②若
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4991ae7c93a141bf73ce7f0b6b7fd7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e709c6565f8241310b97af5e0c831778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f608dd253088da169fb57ad5d1f525c.png)
(1)解同余方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657b55d01c91799ec194df07eea1808e.png)
(2)设(1)中方程的所有正根构成数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c002c44d45907aad22da19859193270b.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39834a599932f7f88a700cc36723a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a1a2133477cd27eed4a945a05d52c7.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8080993903f4969c2dac4a3e01b7123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307cd6a77de16aff5ab0defe75866ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2024-02-28更新
|
2016次组卷
|
4卷引用:江西省红色十校2024届高三下学期2月联考数学试卷
江西省红色十校2024届高三下学期2月联考数学试卷辽宁省沈阳市辽宁实验中学2024届高三下学期高考适应性测试(二)数学试题(已下线)第2套 全真模拟篇 【模块三】(已下线)压轴题07三角函数与正余弦定理压轴题9题型汇总-1
4 . 同余定理是数论中的重要内容.同余的定义为:设a,
,
且
.若
则称a与b关于模m同余,记作
(modm)(“|”为整除符号).
(1)解同余方程
(mod3);
(2)设(1)中方程的所有正根构成数列
,其中
.
①若
(
),数列
的前n项和为
,求
;
②若
(
),求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538f8c7f224b743a48128033066b34cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d71082924d5b4349c3b0152930b7b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a07e47345c46575e63ff4c3df4557bc.png)
(1)解同余方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b31b29e7f0705c981bd91329bcfee7.png)
(2)设(1)中方程的所有正根构成数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c002c44d45907aad22da19859193270b.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addee6ce5163a2580888ce2da22714af.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ac8a1dc1eda952f7145a08c047ebf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.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
2024-02-03更新
|
2836次组卷
|
9卷引用:安徽省合肥市第一中学2024届高三上学期期末质量检测数学试题
安徽省合肥市第一中学2024届高三上学期期末质量检测数学试题(已下线)压轴题函数与导数新定义题(九省联考第19题模式)练(已下线)新题型01 新高考新结构二十一大考点汇总-3(已下线)黄金卷08(2024新题型)(已下线)题型18 4类数列综合浙江省部分学校联考2024届高三高考适应性测试数学试题湖北省武汉市华中师大第一附中2023-2024学年高二下学期数学独立作业(一)重庆市万州二中教育集团2023-2024学年高二下学期入学质量监测数学试题广东省揭阳市普宁市华美实验学校2023-2024学年高二下学期第一次阶段考试数学试题
名校
解题方法
5 . 已知函数
,方程
在
上的解按从小到大的顺序排成数列
.
(1)求数列
的通项公式;
(2)设
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cf40f200ff805e888de812b4fef287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ceeb81f63c3c4e27101d21b34f69d7.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e43ca3db6effb3c3162d96dd7a7f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440afe27e8558f6bf35c8713ce5664b2.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/20bd68513102d1eff5cf1b30b6d61294.png)
您最近一年使用:0次
2022-04-04更新
|
848次组卷
|
5卷引用:江西省八所重点中学2022届高三4月联考数学(理)试题
江西省八所重点中学2022届高三4月联考数学(理)试题山西省长治市第二中学校2022届高三下学期第十二次练考数学(理)试题(已下线)回归教材重难点01 数列-【查漏补缺】2022年高考数学(理)三轮冲刺过关(已下线)文科数学-2022年高考押题预测卷02(全国甲卷)(已下线)5.3 三角函数的性质(精练)-【一隅三反】2023年高考数学一轮复习(提升版)(新高考地区专用)
6 . ①已知数列{
}是递增的等差数列,它的前三项和为9,前三项的积为15.
②已知正项数列{
}的首项
,当n≥2时,有
.
③已知函数
,把方程
的正数解从小到大依次排一列,得到数列{
},n∈N*.
请从以上三个条件中任选一个,完成下列问题.
(1)求数列{
}的通项公式.
(2)记
,设数列{
}的前n项和为Tn,求证:
.
(注:若选择多个条件作答,则按第一个解答计分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
②已知正项数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a413796d8e24d41e48ffb6c706a946d6.png)
③已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89556673cb92c044a892f3fbf79f0a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb15b0bd482fe04e93a32b3930a0c4aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
请从以上三个条件中任选一个,完成下列问题.
(1)求数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efe30d41a6eac4d58312aa39d9c70a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e672c3d231081d12e44a4211e5ac60bf.png)
(注:若选择多个条件作答,则按第一个解答计分)
您最近一年使用:0次
7 . 设等差数列
的前
项和是
,
是各项均为正数的等比数列,且
,
.在①
,②
,③
这三个条件中任选一个,解下列问题:
(1)分别求出数列
和
的通项公式;
(2)若
,求数列
的前
项和
. 注:如果选择多个条件解答,按第一个解答计分.
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc27067aeecc07fc725ce30d3021636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0019a26aae45e4c0565859f1c33b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297304025657b586c73aeabe6eaf25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2e6956e0073cef684fef6a16bead0a.png)
(1)分别求出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1234a0d5f4e82566a46ac382d104fad4.png)
![](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)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.把方程
的正数解从小到大依次排成一列,得到数列
,
.
(1)求数列
的通项公式;
(2)记
,设数列
的前
项和为
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89556673cb92c044a892f3fbf79f0a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19f77669fa0060d1e42fbbcb2ec5042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda0c771434b30a909702c34710e89cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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/e672c3d231081d12e44a4211e5ac60bf.png)
您最近一年使用:0次
9 . 设函数
,方程f(x)=x有唯一的解,
已知f(xn)=xn+1(
)且f(xl)=
.
(1)求证:数列{
)是等差数列;
(2)若
,求Sn=b1+b2+b3+…+bn
(3)在(2)的条件下,是否存在最小正整数m,使得对任意
,有
成立,若存在,求出m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524dc5705d02486d3c65b8b61e7e8f3e.png)
已知f(xn)=xn+1(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b221d7a057f8ee4a029ac0164022db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0e7bfbd56fe73dfe04c04da749d942.png)
(1)求证:数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a3cefbd102e6bdbfc6330e3e599666.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68167cdc71817afdd46bbde959b47f15.png)
(3)在(2)的条件下,是否存在最小正整数m,使得对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b221d7a057f8ee4a029ac0164022db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1346892d59d5818aa4e7e269d44746d.png)
您最近一年使用:0次