名校
解题方法
1 . 记等差数列
的前
项和为
,已知
,且
.
(1)求
;
(2)若对于任意的
恒成立,求实数
的取值范围.
![](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/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc867f18403bdac78525e35c31dec8c7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf32dbdd19b75bd2d2820ebad493f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
2 . 已知公差不为0的等差数列
满足
,且
.
(1)求
的通项公式;
(2)记
是数列
的前
项和,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e186f59e4c84ac1600f710c5c0150f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea4144ba9435a99f0a71a0d526e5517.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13b0d771b3cfd3be92c629d10e90c8e.png)
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2024-06-03更新
|
378次组卷
|
2卷引用:湖南省2024届高三下学期数学模拟试题
3 . 等差数列
的首项为
,公差不为
,若
,
,
成等比数列,则
的前
项的和为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
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解题方法
4 . 2023年的某一天某红酒厂商为了在线出售其红酒产品,联合小Y哥直播间,邀请某“网红”来现场带货.在带货期间,为吸引顾客光临直播间、增加客流量,发起了这样一个活动:如果在直播间进来的顾客中,出现生日相同的顾客,则奖励生日相同的顾客红酒1瓶.假设每个随机来访的顾客的出生日期都是相互独立的,并且每个人都等可能地出生在一年(365天)中任何一天(2023年共365天),在
远小于365时,近似地
,
,其中
.如果要保证直播间至少两个人的生日在同一天的概率不小于
,那么来到直播间的人数最少应该为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa604388a876daaf6a545801e43714d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070f72497850d3f2b5815b363cf459b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4af9de2ed632ca28179b25000efa525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
A.21 | B.22 | C.23 | D.24 |
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名校
解题方法
5 . 已知正项等差数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f0c7910375313c173f0810dca0e500.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f0c7910375313c173f0810dca0e500.png)
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6 . 设等差数列
的前
项和为
,若
,
,则
( )
![](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/22c5c4ac959eb2c4b74afabc9cdd3a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41be41a5a4965ebd346e7ee74d21f0f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614306cc3f34bdee4d5d885b79667645.png)
A.34 | B.35 | C.36 | D.38 |
您最近一年使用:0次
2024-04-01更新
|
951次组卷
|
3卷引用:湖南省湘潭市2024届高三下学期3月质量检测数学试题
23-24高三下·湖南·开学考试
7 . 若数列
满足
,
,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdf53108bee755f5aa9a34ea4d163e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2be148605b1b98bf183b7052eb5657e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77288bfa684c2a9ca00c75743232a0e3.png)
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名校
解题方法
8 . 已知等差数列
满足
,前
项和为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9538ededb840cb0b8a77570e7ee03cca.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/dc4e70b360f988fdbd92300ab22c4613.png)
A.6 | B.10 | C.12 | D.14 |
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9 . 若数列
的前
项和
,则数列
的前
项和
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab8159d658290b9df2453eef6f275b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be67f7ce9d528348fa1cf90208d305c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-02-27更新
|
713次组卷
|
2卷引用:湖南省2024届高三数学新改革提高训练一(九省联考题型)
名校
10 . 已知等差数列
的前
项和为
,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36243198e5e20c56399e4ad5ac3c519.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30bbe131dd67528d219d7507788d35fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb3fdeeb4afe6485ffb00bf83023e704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36243198e5e20c56399e4ad5ac3c519.png)
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2024-02-23更新
|
408次组卷
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2卷引用:湖南省永州市2023-2024学年高二上学期期末质量监测数学试题