1 . 记
(
且
)的展开式中含x项的系数为
,含
项的系数为
.
(1)求
;
(2)若
,对
,3,4成立,求实数a,b,c的值;
(3)对(2)中的实数a,b,c,证明:对任意
且
,
都成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4f819c5714bf76cb6e4cbb5fb64c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048651e049071a622651832e6446a75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
(3)对(2)中的实数a,b,c,证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048651e049071a622651832e6446a75e.png)
您最近一年使用:0次
2023-11-01更新
|
236次组卷
|
7卷引用:2020届江苏省南通市如皋中学高三下学期3月线上模拟考试数学试题
2020届江苏省南通市如皋中学高三下学期3月线上模拟考试数学试题江苏省常州2018届高三上学期期末数学(理)专题20 数学归纳法及其证明-《巅峰冲刺2020年高考之二轮专项提升》[江苏](已下线)专题07 计数原理-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)四川省雅安市天立学校2022-2023学年高二下学期第一次月考数学(理)试题上海市复旦中学2023-2024学年高二上学期期末考试数学试卷(已下线)第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)
20-21高三上·江苏南通·期末
解题方法
2 . 已知函数
,
.
(1)若关于.
的不等式
对任意的
恒成立,求实数
的取值范围;
(2)设
,
.
①求证:
;
②若数列
满足
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc142c4a9f9c8505e7824361a9003099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
(1)若关于.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2475f4a516b408e9c1a1f81bc013b71f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7780ab2eba3eaa3d391a8d5ee712485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2788f2efd111b65f7458002508765c56.png)
②若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4b41419ce9ed61c73bfe422e738c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2c8eb8fd8d5ad456dcf7c3e3279da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d77a6078beed1d99f07c5cbb5ff4484.png)
您最近一年使用:0次
名校
3 . 设正项数列
满足:
,且对于
,都有
,且
.
(1)求
,
;
(2)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee45219629dd30af171588e646f8b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2e39c2deef3fa9ef3d783bc0912ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a106d8500dc27cb020dc351c60083a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2020-08-03更新
|
137次组卷
|
2卷引用:江苏省南通市2020届高三下学期高考考前模拟卷(五)数学试题
解题方法
4 . 已知Sn=1+
+
+…+
.
(1)求S2,S4的值;
(2)若Tn=
,试比较
与Tn的大小,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6a2eba56d4f2d1670b0256b8d86b92.png)
(1)求S2,S4的值;
(2)若Tn=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/688550f4d16d6ad6cfe7da9006f07d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43cd093a4db7ccca329d945748dc2c2.png)
您最近一年使用:0次
名校
5 . 已知数列
满足:
,
,
.
(1)化简:
(结果用
表示).
(2)求证:
,
.
![](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/b5bc50d3e9cacfaff721090ee725ce19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169f26144c7416f654dd1b6952b7573d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c14f644b116359a48b09c0b053ed5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
您最近一年使用:0次
名校
6 . 已知数列
满足:
(常数
),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2a53d3ea259c41ab16e4a4021b1ceb.png)
.数列
满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf6dd9b7ae76500e1daed5f3ec73478.png)
.
(1)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa7631bab118903861195c8c7a2665d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556c0ec1356884663926e9e8deaf5e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52323ee28f3a2cc6a99c89935106e190.png)
的值;
(2)求出数列
的通项公式;
(3)问:数列
的每一项能否均为整数?若能,求出k的所有可能值;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88285bcde29db874f4618af9cae56939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2a53d3ea259c41ab16e4a4021b1ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd67ae4861f074c5c19909af1a0765f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf6dd9b7ae76500e1daed5f3ec73478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fc82353331abee0828dee9b38c08f2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa7631bab118903861195c8c7a2665d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556c0ec1356884663926e9e8deaf5e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52323ee28f3a2cc6a99c89935106e190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
(2)求出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)问:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
您最近一年使用:0次
2020-01-04更新
|
300次组卷
|
2卷引用:江苏省南通市海安高级中学2019-2020学年高三阶段测试三数学试题
9-10高二下·河南·期中
名校
7 . 已知数列
满足
.
(1)写出
,并推测
的表达式;
(2)用数学归纳法证明所得的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf732764ecee2b555071ed13cafae93.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)用数学归纳法证明所得的结论.
您最近一年使用:0次
2022-04-23更新
|
458次组卷
|
14卷引用:2011-2012学年江苏南通第三中学高二下学期期中考试理科数学试卷
(已下线)2011-2012学年江苏南通第三中学高二下学期期中考试理科数学试卷(已下线)2010年河南省实验中学高二下学期期中考试数学(理)(已下线)2011-2012学年广东省惠阳一中实验学校高二下学期3月月考理科数学(已下线)2011-2012学年浙江省嵊泗中学高二第一次月考数学试卷(7-8班)(已下线)2011-2012学年湖北省仙桃市高二下学期期中考试理科数学试卷(已下线)2012-2013学年湖北仙桃毛嘴高中高二上学业水平监测理数学试卷(已下线)2012-2013学年福建省泉州一中高二下学期期中考试理科数学试卷(已下线)同步君人教A版选修2-2第二章2.3数学归纳法山东省菏泽市2016-2017学年高二下学期期中考试数学(理)试题高中数学人教版 选修2-2(理科) 第二章推理与证明 2.3数学归纳法辽宁省营口市开发区第一高级中学2017-2018学年高二下学期第二次月考数学(理)试题天津市红桥区2016-2017学年高二下学期期中理科数学试题山西省晋城市泽州县晋城一中教育集团南岭爱物学校2022-2023学年高二上学期第五次调研考试数学试题1.4 数学归纳法(同步练习基础版)
8 . 已知
,
,
,
.
(1)比较
与
的大小;
(2)比较
与
大小,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e8ba914a6633cc7d473f43d0c00218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6af757812f3d07deb6bb6079df8605c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
(1)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252401d2f21b786f8ce187fff2c4913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41bc13ed73577143311b11a1921a73b.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1331dd807837309346d1763a4101045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f637a84023d386c2fcac750dd4265d.png)
您最近一年使用:0次
9 . 已知函数
,记
,当
时,
.
(1)求证:
在
上为增函数;
(2)对于任意
,判断
在
上的单调性,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0bc4f7ba817dca32178b65d9aab5c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ab7bb40f58f28c9799b20f91d15d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57bdb7eaab39ffa580415a3f0a17ce26.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ace630100e64ed290d82936ad249c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
(2)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
您最近一年使用:0次
2019-10-15更新
|
294次组卷
|
6卷引用:江苏省南通市2018年高考数学模拟试题
江苏省南通市2018年高考数学模拟试题【市级联考】江苏省苏北四市2019届高三第一学期期末考试考前模拟数学试题(已下线)专题6.6 数学归纳法 (练)-浙江版《2020年高考一轮复习讲练测》(已下线)2019年12月11日《每日一题》一轮复习理数-数学归纳法(已下线)专题7.6 数学归纳法(练)-2021年新高考数学一轮复习讲练测(已下线)专题12 导数法巧解单调性问题-备战2022年高考数学一轮复习一网打尽之重点难点突破
名校
10 . 已知数列
满足
…
.
(1)求
,
,
的值;
(2)猜想数列
的通项公式,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e3d3b1bff94d539b712df424554ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc1d31c31c65f8b94214dcac368ad9c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)猜想数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2018-04-20更新
|
1254次组卷
|
3卷引用:江苏省南通市2020届高三下学期6月模拟考试数学试题