1 . 已知数列
各项均为正数,其前
项和为
,且满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcccfaae752f79a14bf7bcf5e405710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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2 . 已知等差数列
的首项
,公差
,且
的第二项、第五项、第十四项成等比数列.
(1)求数列
的通项公式;
(2)设
,记
为数列
的前n项和,求
并说明是否存在最大的整数t,使得对任意的n均有
总成立?若存在,求出t;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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3326e346b0ba15c7a3dd35ebfa025310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227c74d0a68f9ad16ce36e9b20c1feaf.png)
您最近一年使用:0次
2014高三·全国·专题练习
3 . 已知无穷数列
的各项均为正整数,
为数列
的前
项和.
(1)若数列
是等差数列,且对任意正整数
都有
成立,求数列
的通项公式;
(2)对任意正整数
,从集合
中不重复地任取若干个数,这些数之间经过加减运算后所得数的绝对值为互不相同的正整数,且这些正整数与
一起恰好是1至
全体正整数组成的集合.
(ⅰ)求
的值;(ⅱ)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](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)
(1)若数列
![](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/5bb49a3acf1f51949a97e5e79da67d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7eba6dff8aeb6e558d01c3e10b1b2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2016-12-02更新
|
1531次组卷
|
3卷引用:2015届湖南省长沙市高考模拟理科数学试卷
4 . 已知数列
是等差数列,其前
项和为
,数列
是等比数列,并且
,
.
(1)求数列
和
的通项公式;
(2)设
,求数列
的前
项和
.
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f478acd1cb5b5a7f66d10b4f318d78d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dbb10cee9a722f6551d6ee4f41ca84.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cbc636c8f8bc4722068ad67968e14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2016-12-04更新
|
312次组卷
|
3卷引用:湖南省长沙市长郡中学2018届高三月考试题(二)数学(理科)试题
名校
解题方法
5 . 若有穷数列
(
是正整数),满足
即
(
是正整数,且
),就称该数列为“对称数列”.例如,数列
与数列
都是“对称数列”.
(1)已知数列
是项数为9的对称数列,且
,
,
,
,
成等差数列,
,
,试求
,
,
,
,并求前9项和
.
(2)若
是项数为
的对称数列,且
构成首项为31,公差为
的等差数列,数列
前
项和为
,则当
为何值时,
取到最大值?最大值为多少?
(3)设
是
项的“对称数列”,其中
是首项为1,公比为2的等比数列.求
前
项的和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb97979f93c90fcf4baa7b7106abb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7953bb514daa500885e892857678f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22fc26a14e8e5987688565881fb71e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b266d811e20740699ab629767b43e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1122d70cf267893185983de9d811729.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f6714682274c31a328bf796e235900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc5a47eb206ee12c7f65ea26fc26e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64fcc69dc28bc11b22f5c9bec9e2aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ada2c9f82459340da96274ee60ffbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cba4fcd5b19e52391aa57127aa39b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0fcf02ab751cc3910a0bc0872ac2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05201ef79a5d5904f492845396fb5470.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8746bc092f553f33ce1a0d8d2b7b28d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be881773917095d173260995ffacfd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897d8f6cf00391f1b3ff70432f0121b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31ec8dee46f3affe69cbdb2abbe8feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31ec8dee46f3affe69cbdb2abbe8feb.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50d1705a68b70921f86dd10020420b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24de9307bdb075bfc55d86d35e54ed57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50d1705a68b70921f86dd10020420b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f1dd3b69d0e8157998cc59efedb022.png)
您最近一年使用:0次
2017-07-02更新
|
219次组卷
|
2卷引用:湖南省长沙市明德中学2016-2017学年高二上学期阶段测试数学试题