1 . 已知曲线
.从点
向曲线
引斜率为
的切线
,切点为
.
(1)求数列
的通项公式;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367ea5a90d6a71014732170bd5246bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f7f821e9bd307002f782274e0b990b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bfc7cc4778317e79847f46ccf41a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7c5e7bd6bac51402ffa04b4144ec78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9979465ce76b8582067703b39a0bc6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e09b1efea919a67599f681b4ee8e1.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c64a598e602dc1a816c0e9d389fd7994.png)
您最近一年使用:0次
2 . 已知函数
对任意
,都有
.
(1)求
和
的值;
(2)若数列
满足:
则数列
是等差数列吗?请给予证明.
(3)令![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/0329244e4c17444ab0ea26d6b7c743d0.png)
,试比较
与
的大小.
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/323e63a3cd874400bda17290ca175694.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/ccc3864712eb47f09f122c7a9e571d08.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/4ceafa0809e94a6fac0cdec887398ed4.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/113449bb8f42489abe72a63359159c94.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/f8b1bda9878443baa59f56170a4cb401.png)
(2)若数列
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/f2d18a2126324c528a8d1b708c48ee8f.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/5b372179691c41dd95482435d852809f.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/f2d18a2126324c528a8d1b708c48ee8f.png)
(3)令
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/0329244e4c17444ab0ea26d6b7c743d0.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/0c649e2675bd4062979318cb3c8fa332.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/449bb88f84df46aa9f4201ca7c8471cd.png)
![](https://img.xkw.com/dksih/QBM/2012/3/27/1570821801287680/1570821806637056/STEM/94028479b758459784068e66b8425212.png)
您最近一年使用:0次
2011·广东茂名·一模
3 . 已知数列
满足
,且
.
(Ⅰ)求证:数列
是等差数列,并求通项
;
(Ⅱ)若
,且
,求和
;
(Ⅲ)比较
与
的大小,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2d4ee4ca59ee21a52cdc88b8a7f994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5a507879ed62acd7cfec1dbbfe91c1.png)
(Ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d17a1ac79d2fbc8481e319a64c11e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6372af2da3bc6ce6cda193a79a88c975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7af884c9717e1584d130525fdda61815.png)
(Ⅲ)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2855e9b353277395dbfcea8e568182ea.png)
您最近一年使用:0次