如图,已知曲线
及曲线
.从
上的点
作直线平行于
轴,交曲线
于点
,再从点
作直线平行于
轴,交曲线
于点
,点
的横坐标构成数列
.
与
之间的关系,并证明:
;
(2)若
,求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af82160c02868bb45fc65d7597c84027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39da03b091bb40dd965458631bf50786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0fb5c4c19ac84d269620933529d592d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76717a33aa190b392c6a3badea1aaaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89cd245dba055034203e2450ba9b8848.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
2023·湖南长沙·一模 查看更多[9]
湖南师范大学附属中学2023届高三一模数学试题专题13数列(解答题)(已下线)第三篇 数列、排列与组合 专题1 建立递推关系求通项公式 微点2 建立递推关系求通项公式综合训练辽宁省沈阳市浑南区东北育才学校科学高中部2023-2024学年高三上学期高考适应性测试(一)数学试题(已下线)第五章 数 列 专题1 数列中的不等关系的证明(已下线)第五章 数列 专题1 数列中的不等关系的证明(已下线)第04讲 数列的通项公式(十六大题型)(讲义)-4(已下线)专题09 数列的通项公式、数列求和及综合应用(练习)-2(已下线)压轴题05数列压轴题15题型汇总-3
更新时间:2023-05-23 16:34:56
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解答题-问答题
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名校
【推荐1】某游戏棋盘上标有第
、
、
、
、
站,棋子开始位于第
站,选手抛掷均匀硬币进行游戏,若掷出正面,棋子向前跳出一站;若掷出反面,棋子向前跳出两站,直到跳到第
站或第
站时,游戏结束.设游戏过程中棋子出现在第
站的概率为
.
(1)当游戏开始时,若抛掷均匀硬币
次后,求棋子所走站数之和
的分布列与数学期望;
(2)证明:
;
(3)若最终棋子落在第
站,则记选手落败,若最终棋子落在第
站,则记选手获胜.请分析这个游戏是否公平.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9ba3f640f57c0cece089dfd19b4970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(1)当游戏开始时,若抛掷均匀硬币
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60fa61313854fd089befc190ff640d10.png)
(3)若最终棋子落在第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9ba3f640f57c0cece089dfd19b4970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
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(0.4)
【推荐2】已知函数f(x)=ex﹣e﹣x,g(x)=ax(e为自然对数的底数),其中a∈R.
(1)试讨论函数F(x)=f(x)﹣g(x)的单调性;
(2)当a=2时,记函数f(x),g(x)的图象分别为曲线C1,C2.在C2上取点Pn(xn,yn)作x轴的垂线交C1于Qn,再过点Qn作y轴的垂线交C2于Pn+1(xn+1,yn+1)(n∈N*),且x1=1.
①用xn表示xn+1;
②设数列{xn}和{lnxn}的前n项和分别为Sn,Tn,求证:Sn﹣Tn+1>nln2.
(1)试讨论函数F(x)=f(x)﹣g(x)的单调性;
(2)当a=2时,记函数f(x),g(x)的图象分别为曲线C1,C2.在C2上取点Pn(xn,yn)作x轴的垂线交C1于Qn,再过点Qn作y轴的垂线交C2于Pn+1(xn+1,yn+1)(n∈N*),且x1=1.
①用xn表示xn+1;
②设数列{xn}和{lnxn}的前n项和分别为Sn,Tn,求证:Sn﹣Tn+1>nln2.
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【推荐1】已知数列
满足:
,且
.
(1)求证:数列
是等比数列;
(2)设
是数列
的前
项和,若
对任意
都成立.试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c2d19d6b259f57f4659e8643e02a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c044e907c418159ff0b98c5fea4dc748.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](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/a0823d78ca3873c8a070208d54cf716b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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【推荐2】在各项均为正数的等比数列
中,
,且
成等差数列.
(1)求等比数列
的通项公式;
(2)若数列
满足
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/488311bf2d495245f4fa3179b7d7cb83.png)
(1)求等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bd6ccba42f65da72f6867455c74599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a2ebd0a97c7ec566cc065abe557cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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【推荐1】甲、乙两名小朋友,每人手中各有3张龙年纪念卡片,其中甲手中的3张卡片为1张金色和2张银色,乙手中的3张卡片都是金色的,现在两人各从自己的卡片中随机取1张,去与对方交换,重复
次这样的操作,记甲手中银色纪念卡片
张,恰有2张银色纪念卡片的概率为
,恰有1张银色纪念卡片的概率为
.
(1)求
的值.
(2)问操作几次甲手中银色纪念卡片就可能首次出现0张,求首次出现这种情况的概率
.
(3)记
.
(i)证明数列
为等比数列,并求出
的通项公式.
(ii)求
的分布列及数学期望.(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce603aa3abcb61750d2191aaa13dddc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f66b7e38f44f8cd5d48b3aa24a20fc.png)
(2)问操作几次甲手中银色纪念卡片就可能首次出现0张,求首次出现这种情况的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9131abf93295537bbc0c54a8c42e88e2.png)
(i)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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【推荐2】函数
对所有实数
都满足:①
;②
;③
.
(1)求证:
为常数
;
(2)设数列
,求证:
是等差数列,并求
;
(3)若
,求证:
是等比数列;
(4)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c3c1ed4fb65ab9505ad8078d8d0fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b211c7242dd0b39d6992253f765101a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c5248be3989b50d38d3d4f7a8f4fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78510a5bed526a4c63c492e86e6a55ac.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd403b6c023d2c2a5d6e7ddc5866e258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035937c12508091015aefe47f6c50519.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d68e2dec6a32ad132fc40de9e4aa506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce5dc16de6aa68888e0d7885820e0a0a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8253c3b09173d2ee17410c226649bd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(4)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe80c9a0161a58601f091c5a8ff6951.png)
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解答题-问答题
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较难
(0.4)
解题方法
【推荐1】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1d7268da9d714fed3affcc7d584ccc.png)
的图像在点
处的切线与直线
垂直.
(1)
满足的关系式;
(2)若
在
上恒成立,求
的取值范围;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1d7268da9d714fed3affcc7d584ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9cd3690e7aa3debb1ed054a9f622da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfc6b5b7ae63a330f0cd8593ee47338.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459675388f702277c9c19bf19c369c86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec8598505f12bb9dd38f050ca7cd7af.png)
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【推荐2】已知等差数列
与等比数列
满足
,
,
.
(1)求数列
,
的通项公式;
(2)若
,求证:
.
![](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/c528a7cdaf941c327989a194e429c48e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e176bf5db8bc1f540796220a08d96e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a72334b6680e5c994ca5f825062e19.png)
(1)求数列
![](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/e712f42fa33fefef00795afaa26b3a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710044de63cdfc94812bafb3cc54b7c2.png)
您最近一年使用:0次