解题方法
1 . 已知数列
的前
项和为
,且满足
,且
.
(1)求证:数列
为常数列,并求
的通项公式;
(2)若使不等式
成立的最小整数为
,且
,求
和
的最小值.
![](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/80a51fdb3d97b50142146e1323d38fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d184bbed41bf722800038b31fa82ef.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9005e40f6d18bdda17831b849b36f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若使不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7b88174caa1380678186c1189f1624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f3041a8e109178d9754f6ff98d70d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-03-10更新
|
978次组卷
|
3卷引用:广西平果市铝城中学2023-2024学年高二上学期期末预测数学试题
名校
解题方法
2 . 在①
,
;②
,
,③
,
这三个条件中任选一个,补充在下面问题中并解决问题.
问题:设等差数列
的前
项和为
,________________,若,判断
是否存在最大值,若存在,求出
取最大值时
的值;若不存在,说明理由.
注:如果选择多个条件分别解答.按第一个解答记分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b83d73d014a0ca4aff4282228312f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d245ef59a9f267a551acd8d1df4082a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a2885e3fb2d5501fdd07005568a0b99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2042ea708238250fd73ca88f8cebad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df7fe8cd58a89cef831601f361c6c23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee92298a0a93de40f051e1bfbafdb95.png)
问题:设等差数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
注:如果选择多个条件分别解答.按第一个解答记分.
您最近一年使用:0次
2021-05-14更新
|
1104次组卷
|
5卷引用:福建省莆田第一中学2021-2022学年高二上学期期末考试数学试题
福建省莆田第一中学2021-2022学年高二上学期期末考试数学试题河北省石家庄市2021届高三二模数学试题(已下线)专题7.3 等差数列的前n项和-2022届高三数学一轮复习精讲精练(已下线)一轮复习大题专练33—数列(结构不良型问题)-2022届高三数学一轮复习(已下线)专题5 等差数列的单调性和前n项和的最值问题 微点2 等差数列前n项和的最值的求法
解题方法
3 . 已知各项均为正数的等比数列
中,
,且
.
(1)求数列
的通项公式;
(2)设
是数列
的前
项和,求使得
恒成立的正整数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65c44af8125cfd1e8c9a6d2985bcee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69b1b3aaaa43665d9abbe58549bbad5.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917c211671ea88b7081c3ca517df0dc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440d775091e88627fa6c2cf2eae476df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
4 . 已知无穷等比数列
中,首项
,公比
,数列
满足
.
(1)求数列
的通项公式;
(2)求数列
的前n项和的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f5e92567d0dba659105b4ac9516a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d70671c760a167c1bae433c1d0c433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63cadeae0a46129f23131a08a250e7f4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
名校
5 . 记
为等差数列
的前
项和,已知
,
.
(Ⅰ)求
的通项公式;
(Ⅱ)求
,并求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a283cf860a5ae70a1d4f30cb655d1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da79e928b881e1d26b885c3f5f3f75f2.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
您最近一年使用:0次
2018-11-18更新
|
1025次组卷
|
5卷引用:【全国县级联考】河北省邯郸市鸡泽、曲周、邱县、馆陶四县2017-2018学年高二下学期期末联考数学(理)试题