1 . 已知等差数列
的公差为
,前
项和为
,现给出下列三个条件:①
,
,
成等比数列;②
;③
.请你从这三个条件中任选两个解答下列问题.
(1)求
的通项公式;
(2)若
,且
,设数列
的前
项和
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bfe21c96489cb30c544d49ddb4c1c8.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/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2cb4485663835fc40a9cf82f491d5b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8e6faeb947f20b486c3c888f1cd7e8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7061a937daa71bec578d89117a507ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4995fa0403e013d888c0935ebfe15024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5428b5ba92348081c866a7bf500bd315.png)
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4卷引用:四川省成都市第七中学2022-2023学年高三上学期12月阶段性测试数学(文)试题
四川省成都市第七中学2022-2023学年高三上学期12月阶段性测试数学(文)试题四川省成都市第七中学2022-2023学年高三上学期12月阶段性测试数学(理)试题(已下线)技巧04 结构不良问题解题策略(精讲精练)-2(已下线)拓展二:数列求和方法归纳(3)
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解题方法
2 . 已知函数
.
(1)当
对,求函数
的最小值;
(2)若
对
恒成立,求实数
取值集合;
(3)求证:对
,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0daab460e2b22642d1e1c25e138145b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72620c113a6fe83273803a9ac24baa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2c1f263350273b17c2b2f69c23ad55.png)
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2卷引用:四川省成都市第七中学2022-2023学年高三上学期12月阶段性测试数学(文)试题
3 . 如图,在梯形
中,
,
,
,四边形
为矩形,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/2021/10/23/2835675706736640/2836060223062016/STEM/5a1b02c405cc4568b0bd8d0acd3332f3.png?resizew=202)
(1)求证:
平面
,
平面
;
(2)点
在线段
上运动,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a75b1354b8b783a65ee5e3bc596a976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e904f5b316b9ba89599fb789dd9b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7789714521fb2a5e9e5167d845449c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4280be91682e5d8a0d0704190319bb.png)
![](https://img.xkw.com/dksih/QBM/2021/10/23/2835675706736640/2836060223062016/STEM/5a1b02c405cc4568b0bd8d0acd3332f3.png?resizew=202)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9b32570d553161be04d13954e92a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10c16d2d9d22c4b34ddd965e26aa0d7.png)
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3卷引用:四川省成都市第七中学2022-2023学年高三上学期12月阶段性测试数学(文)试题
四川省成都市第七中学2022-2023学年高三上学期12月阶段性测试数学(文)试题(已下线)专题9.2—立体几何—表面积与体积2—2022届高三数学一轮复习精讲精练四川省成都市树德中学2021-2022学年高三上学期10月阶段性测试数学(文)试题