名校
1 . 数列
的通项公式
,记
为
在区间
中的项的个数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908944f7b075838a91c0e187f6a23324.png)
______ ,数列
的前100项的和等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c7688fdbb166d2171c9b952d09c7f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915daa6700ee4507fd074b085703522f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2486e4fb67c07247e047c369a915c117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908944f7b075838a91c0e187f6a23324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a03df1834d8b96da4bb3bdf18e49b4.png)
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2 . 定义在
上的函数
满足
,
,已知
,则数列
的前
项和______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d54d72fc7ddac261ba98567543d940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c71798873dbc4fe207beab516907087c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b72ac611ae66b86761e080761d9aabc.png)
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3 . 已知数列
,
满足
,
,
,
的前n项和为
,前n项积为
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16a66d7fe18e7803b65e61f7b3e52fc.png)
______ .
![](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/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a413ff3d71c30b0f0414f1b30ceafa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b82ac1c337712192577fcd7434a56d1.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16a66d7fe18e7803b65e61f7b3e52fc.png)
您最近一年使用:0次
2022-05-26更新
|
1071次组卷
|
4卷引用:辽宁省沈阳市市级重点高中联合体2021-2022学年高二下学期期中考试数学测试题
辽宁省沈阳市市级重点高中联合体2021-2022学年高二下学期期中考试数学测试题(已下线)专题4求和运算 (提升版)安徽省滁州市定远县民族中学2021-2022学年高二下学期5月月考数学(理)试题(已下线)4.1数列(第2课时)(分层作业)(2)
4 . 已知数列
,
的通项公式分别为
,
,现从数列
中剔除
与
的公共项后,将余下的项按照从小到大的顺序进行排列,得到新的数列
,则数列
的前150项之和为( )
![](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/9260f8989cfd0ffca5a49ffbc0668f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267c99ff3f6386113dbaa7b1e49612da.png)
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
A.23804 | B.23946 | C.24100 | D.24612 |
您最近一年使用:0次
解题方法
5 . 设各项非零的数列
的前
项和记为
,记
,且满足
.
(1)求
的值,证明数列
为等差数列并求
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/206cc1e86309d8fd0bde20c3661dc89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04952517d62c9cdc0c60344a42fa5033.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ba36c083d3c4a0f79cd45abf5815f19.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/aae6358af7332d7609bf8d18467487d3.png)
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6 . 在数列
中,
,且
.
(1)证明:
为等比数列,并求
的通项公式;
(2)令
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6065aaa8f3f103d1bc960da8318ce35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45afd2aa9695d0c53c3f61dda4034955.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9be5bf50c5db10bdfef370807b0104d.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
7 . 对于正整数n,
是小于或等于n的正整数中与n互质的数的数目.函数
以其首名研究者欧拉命名,称为欧拉函数,例如
(1,2,4,5,7,8与9互质),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f712cbba4784c56c3907626521a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f712cbba4784c56c3907626521a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce8beee7022af5babe15d32d07fde7a.png)
A.若n为质数,则![]() | B.数列![]() |
C.数列![]() ![]() | D.数列![]() |
您最近一年使用:0次
2022-04-14更新
|
1161次组卷
|
3卷引用:湖南省长沙市第一中学2022届高三下学期月考(九)数学试题
2022高三·全国·专题练习
名校
8 . 设曲线
在点
处的切线与
轴的交点的横坐标为
,令
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dff493c112cf0c5a68a01b608702a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981a8903d978a1588f786cfd54d80785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d6aef836c4aca7d6b37e9477f50e06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78ffa29ebabab00d72fbd0b97996d9a.png)
A.2 020 | B.2 019 | C.1 | D.-1 |
您最近一年使用:0次
名校
9 . 已知数列{
}的通项公式为
,前n项和为
,当
取得最小值时,n的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d87ed8c93c3821c122b4eeded16bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2022-02-05更新
|
452次组卷
|
2卷引用:江苏省常州市溧阳市2021-2022学年高二上学期期末数学试题
10 . 在①
,
;②公差为1,且
成等比数列;③
,
,三个条件中任选一个,补充在下面问题中,并给出解答.
问题:已知等差数列
的前
项和为
,且满足___________
(1)求数列
的通项公式;
(2)令
,其中
表示不超过
的最大整数,求
.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36183db0759eec0e108274d229fcd00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca2cc2768794136c1e4da47d2f0873e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b1b845916a4b6a18cdfbcd308d09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11872e2a261f126308bb4e8f3c2ad33.png)
问题:已知等差数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad810e3e145f58d5c569dcaed7df0224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a47750f1d97fb5d63669836a0927c60.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2022-01-22更新
|
821次组卷
|
4卷引用:山东省临沂市2021-2022学年高二上学期期末数学试题
山东省临沂市2021-2022学年高二上学期期末数学试题 江苏省宿迁中学2022-2023学年高二下学期入学检测数学试题山东省东营市第一中学2022-2023学年高二下学期开学摸底检测数学试题(已下线)第四章 数列(A卷·知识通关练) (2)