真题
解题方法
1 . A是由定义在
上且满足如下条件的函数
组成的集合:①对任意的
,都有
;②存在常数
,使得对任意的
,都有
.
(1)设
,证明:
;
(2)设
,如果存在
,使得
,那么这样的
是唯一的;
(3)设
,任取
,令
,证明:给定正整数k,对任意的正整数p,不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de71d25c72850e383a4c841eed0db99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2775ffdf695af2d263f0ea93ac5904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4031c9cbbcbbecfc0a8ca5490647e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5d880d349c00a3f81f830bb35e1d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d03b29af4e3206af656a142d17657f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799650ddf5fb8e7c91cf59163aa1b7a4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1dbdb8423d86a92629b081ae2b2154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0324fecb070287715e3e8f2322056922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5528f643fe7e0449e48c8f81b16b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e599070e5874ed4a9478f5260b98e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0d7024ce3371628f09963f9a976ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dcca902b1982e13aeea5d094bb6016.png)
您最近一年使用:0次
真题
2 . 数列{an}满足:a1+2a2+…nan=4﹣
,n∈N+.
(1)求a3的值;
(2)求数列{an}的前 n项和Tn;
(3)令b1=a1,bn=
+(1+
+
+…+
)an(n≥2),证明:数列{bn}的前n项和Sn满足Sn<2+2lnn.
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572144872194048/1572144878157824/STEM/5a8c62d42da34219aa18e299d795d1e2.png)
(1)求a3的值;
(2)求数列{an}的前 n项和Tn;
(3)令b1=a1,bn=
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572144872194048/1572144878157824/STEM/7165218638a24bf88d846b8910291f03.png)
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572144872194048/1572144878157824/STEM/e90b83438f794ec29f97b768829d1af3.png)
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572144872194048/1572144878157824/STEM/df4e1eae169444d5b6abe4c5e4342b35.png)
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572144872194048/1572144878157824/STEM/6cb19848f7f84d939831ce6d01081554.png)
您最近一年使用:0次
真题
解题方法
3 . 设
,数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ac63c45383e1b0a80afbe8cb0adcbb.png)
(1)求数列
的通项公式;
(2)证明:对于一切正整数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5e02bef0f92246b375f559143bc9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ac63c45383e1b0a80afbe8cb0adcbb.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:对于一切正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19b8ef4193d4c8c4c8944f8c02d7f37.png)
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4 . 在平面直角坐标系
中,给定抛物线
,实数
满足
,
是方程
的两根,记
(1)过点
作
的切线交
轴于点
,证明:对线段
上的任一点
,均有
;
(2)设
是定点,其中
满足
,过
作
的两条切线
,切点分别为
,
与
轴分别交于
,线段
上异于两端点的点集记为
,证明:
;
(3)设
,当点
取遍
时,求
的最小值(记为
)和最大值(记为
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423dd554f7aeb16125a504a184475cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772afcc01c1403c748a0309e864cc61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969eb127024cc1af1f9bf025a65270b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3fb59a42bef86feafb85a91ac571bf.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8817cd9512dbb13ec1b51fc08f24665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcfcaf60bec2f8e1f983f46380d71e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe069597c109e716479c9296cf3ebcb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe689f915e3c9c12616966d1a9a9352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2714a73764c5e100793c925f5812aad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c862b6389bc63a67c0e3cc86466e1269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1871c2be51c597ca28acb6dd8555bf.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de41f1cac6a2d9a98ec52a72a18283b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2542208be649a40105724802a7ad10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3934126cd86a6bf079a2650e5f79979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a0c8b7d066e9d3b9a4db3161b74df1.png)
您最近一年使用:0次
5 . 设p,q为实数,α,β是方程
的两个实根,数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0e11804363c5633b2c35725f5cc57e.png)
(1)证明:
;
(2)求数列
的通项公式;
(3)若
求
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969eb127024cc1af1f9bf025a65270b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0e11804363c5633b2c35725f5cc57e.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d105505a3abfd9ff8cd51738733cc2.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5243512602295eecace014d2c50a9f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2016-11-30更新
|
1772次组卷
|
6卷引用:2008年普通高等学校招生全国统一考试理科数学(广东卷)
2008年普通高等学校招生全国统一考试理科数学(广东卷)2008 年普通高等学校招生考试数学(理)试题(广东卷)(已下线)考点25 数列求和-备战2022年高考数学(理)一轮复习考点帮(已下线)第三篇 数列、排列与组合 专题3 数列的特征方程 微点1 数列的特征方程(已下线)第三篇 数列、排列与组合 专题9 发生函数 微点1 利用发生函数解决数列问题(已下线)专题10 数列通项公式的求法 微点9 特征根法
6 . 已知函数
,
是方程
的两个根
,
是
的导数.设
,
.
(1)求
的值;
(2)证明:对任意的正整数n,都有
>
;
(3)记
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc565280dff5e2d9eba14fe31b72ae31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb33baa166bf2101650f6810892e9af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39108bd0e8876ff6dfd2fe70c83136c2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
(2)证明:对任意的正整数n,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e864ce69fc9f5dd73b01fa2308affac3.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)
您最近一年使用:0次
2016-11-30更新
|
2230次组卷
|
5卷引用:2007年普通高等学校招生全国统一考试理科数学卷广东
2007年普通高等学校招生全国统一考试理科数学卷广东2007年普通高等学校招生考试数学(理)试题(广东卷)(已下线)第三篇 数列、排列与组合 专题4 数列的不动点 微点2 数列的不动点(二)(已下线)第三篇 数列、排列与组合 专题5 迭代数列与极限 微点5 迭代数列与蛛网图(已下线)专题10 数列通项公式的求法 微点8 不动点法