数列
中,
.
(1)证明:
;
(2)证明:
;
(3)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f988528c769abf297a7e6c90aef84d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a5945ce5c2114af8c18718ca8dc899.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5447e912054cedfe70ae90cb965ee9ad.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d4c05017b9179c487c57bb73110207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b26af799e8abfccebce5e83e5dc6e7.png)
更新时间:2017-08-15 13:55:53
|
相似题推荐
解答题-证明题
|
困难
(0.15)
【推荐1】若数列
在某项之后的所有项均为一常数,则称
是“最终常数列”.已知对任意
,函数
和数列
满足
.
(1)当
时,证明:
是“最终常数列”;
(2)设数列
满足
,对任意正整数
.若方程
无实根,证明:
不是“最终常数列”的充要条件是:对任意正整数
,
;
(3)若
不是“最终常数列”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc6de641322c6aeb24e0bbd875e65b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3980f4d5c5ec0f551d7a3c3c0b5ffdc7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b26218ecae19cc13017d561c01d69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36737370e7f4231ebdd27c957f47f45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8f2cc86844dc647bfb33344781e75a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66c77ea288be5bfb4445a76a2429aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
解答题-问答题
|
困难
(0.15)
名校
【推荐2】已知
和
是各项均为正整数的无穷数列,如果同时满足下面两个条件:
①
和
都是递增数列;
②
中任意两个不同的项的和不是
中的项.
则称
被
屏蔽,记作
.
(1)若
,
.
(i)判断
是否成立,并说明理由;
(ii)判断
是否成立,并说明理由.
(2)设
是首项为正偶数,公差是
的无穷等差数列,判断是否存在数列
,使得
.如果存在,写出一个符合要求的数列
;如果不存在,说明理由;
(3)设
是取值于正整数集的无穷递增数列,且对任意正整数
,存在正整数
,使得
.证明:存在数列
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
则称
![](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/1284d81cf684a54e3070d2c69085c76e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e46ecd051c92489c0d1d458932f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fef6975d285cabcf6be67c78f30d30.png)
(i)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
(ii)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b5bb0902c0daf52fe26a78a250b96f7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33f575cee1cddd9bbc34dcd592a4e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53442dcf82f93d94f20be6bf2c934cb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
您最近一年使用:0次
【推荐1】已知数列
,
,
满足:
,
.
(1)若
是等差数列,且公差
,求数列
的通项公式
;
(2)若
、
均是等差数列,且数列
的公差
,
,求数列
的通项公式.
![](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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0846ab503f3451d5dd0cef4852cc0bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f5556e06ca9c3ea36ed3ad7908994e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8a247d65b33fb596e32cff36fbd96a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc0affca4a869b7876243731cfd00e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a31a2bfcc245c76122d7d8fc0d8012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
解答题-证明题
|
困难
(0.15)
名校
【推荐2】已知数列
,
满足:
.
(1)若
,求数列
的通项公式;
(2)若
,且
.
① 记
,求证:数列
为等差数列;
② 若数列
中任意一项的值均未在该数列中重复出现无数次,求首项
应满足的条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3249883fe3dab15d47302fef4f37146b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3473964e962ac6304ee4a66a239f9e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93d57876a4346a2c065c1c2c69e6510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e19845d07c89edf3424ef3caf45810.png)
① 记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a79cf657c6b6d301bfd1e748bff12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
② 若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245588805f41199996befd1d3d5c7c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
解答题-证明题
|
困难
(0.15)
【推荐1】已知
为正整数数列,满足
.记
.定义A的伴随数列
如下:
①
;
②
,其中
.
(1)若数列A:4,3,2,1,直接写出相应的伴随数列
;
(2)当
时,若
,求证:
;
(3)当
时,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97559b8ae5f9544c7b93bf2f9d03394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6559598727fb120a5cdbf4f15510615d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c995ba5a9caa036977b023f57a4202f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271c5044aeaf0fd2a6f75746754565c8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880b1efd3798a3ccf2633252b10e0ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570d7b5b193a644beb91889bbde27cde.png)
(1)若数列A:4,3,2,1,直接写出相应的伴随数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3053e2b8a6bbc35527a1e4505b84ed0f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2578cb9428c41fa9236c6350bae49f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941e10d4febad08273c2b181023f019f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2578cb9428c41fa9236c6350bae49f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fac29b7c846a7ba3b612b0f7ebee41.png)
您最近一年使用:0次
解答题-证明题
|
困难
(0.15)
名校
解题方法
【推荐2】(1)证明:当
时,
;
(2)已知正项数列
满足
.
(i)证明:数列
为递增数列;
(ii)证明:若
,则对任意正整数
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca947e8ea00b7a485097ecafd2dfcae9.png)
(2)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f91f8b7476e67db488d85c3a14ffa6d.png)
(i)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
(ii)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f2db682457da2d4abd0e7cca1bdf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d8a310323506a3c2f3626dec8d781f.png)
您最近一年使用:0次
解答题-证明题
|
困难
(0.15)
名校
【推荐1】已知函数
,
.
(1)讨论
的单调区间;
(2)当
时,令
.
①证明:当
时,
;
②若数列
满足
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeea9bb195a844feb2f1806db8259604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ee7c7dd3a775fa701366908859c614.png)
①证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd791cdf876b9a9e58f251f803aeb66.png)
②若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6f4a302d3a9023c0a82b889f4ba918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92903b4ad4fc018c9f7d0309ed20403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63554d67f64c68adbd28bce22fb79b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7378e6e95cfe560f97ec0e7951e15a.png)
您最近一年使用:0次
【推荐2】已知在每一项均不为0的数列
中,
,且
(
、
为常数,
),记数列
的前
项和为
.
(1)当
时,求
;
(2)当
、
时,
①求证:数列
为等比数列;
②是否存在正整数
,使得不等式
对任意
恒成立?若存在,求出
的最小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639a6bb038215e3615f53ce2faf9f93f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.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)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
①求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ccf5dbc6bf9cab46c3c9a6a11c84fcd.png)
②是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ecce6bf54d9afecb470ce2469397cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次