1 . 证明下列不等式
(1)已知
,
,
,且
,求证:
.
(2)已知
,
,
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cad3aaeb5b444feb152378278f68863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cc7582a7b091b3f0f5a51325e1d0a1.png)
您最近一年使用:0次
解题方法
2 . (1)
,其中x,y均为正实数,比较a,b的大小;
(2)证明:已知
,且
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ff50e53d35f0c88f9ba8b5ba681d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec33f3dd246b2deec64c7c40b9b2d663.png)
(2)证明:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ff50e53d35f0c88f9ba8b5ba681d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882a6e8f86e28c2382ab50e2c8ab0c0c.png)
您最近一年使用:0次
名校
解题方法
3 . 已知数列
的前
项积为
,且
.
(1)求证:数列
是等差数列;
(2)证明:
.
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3406df6552d66166d04a3d22e2f86929.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a40442811c08c432ec613102e4502c0.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031efafb3886a33f3ac39fc85eab869d.png)
您最近一年使用:0次
2023-10-13更新
|
1982次组卷
|
4卷引用:江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题
江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期教学质量调研(一)数学试题江苏省连云港市部分学校2023-2024学年高三上学期10月第二次学情检测数学试题江苏省南京市江宁区东山高级中学三校联考2023-2024学年高三上学期期中调研考试数学试题
解题方法
4 . (1)已知
,设
,
,比较
与
的大小;
(2)证明:已知
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec532f119aff0491334d43cf6b1adf70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1166d36cb26ddb11b666ad0faf6a8b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)证明:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a0aa068c979c53361d049ce49987a8.png)
您最近一年使用:0次
解题方法
5 . 证明下列不等式:
(1)已知
,求证:
;
(2)已知
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9656db3a38e6c58dc5ceb291173053a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829e09e0f8adbcb6ca7e8902019729f6.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc2bb608dcbe043ded3b74d4a8b5140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d2a05075997525049a368aba1c2b46.png)
您最近一年使用:0次
6 . 已知正项数列
的前
项和为
,
.
(1)记
,证明:数列
的前
项和
;
(2)若
,求证:数列
为等差数列,并求
的通项公式.
![](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/039e4fe671d61e59b96ee525c9df43e8.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf114725ab617af515bf9d2571402106.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/f9928e46511e601913619a427ded84a3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7e6e9c815b0716de4f5515e4370f77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2023-08-29更新
|
808次组卷
|
3卷引用:浙江省A9协作体2023-2024学年高三上学期暑假返校联考数学试题
解题方法
7 . (1)已知
,求证
;
(2)利用(1)的结论,证明:
(
且
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e793a22eefbb0c5252b15dac42a0769.png)
(2)利用(1)的结论,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb38b30ef5a3de081c41f92ad2992b7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
您最近一年使用:0次
8 . 已知数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
是否是等比数列?若是,给出证明;否则,请说明理由;
(2)若数列
的前10项和为361,记
,数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04053ecf80b3bb9179c8baab47bf8dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc0cf1f0a00718b95a2a4fffd11dd32.png)
您最近一年使用:0次
2023-08-20更新
|
2537次组卷
|
9卷引用:湖北省高中名校联盟2024届高三上学期第一次联合测评数学试题
9 . 已知各项均不为零的数列
的前n项为为
,且满足
.
(1)证明:数列
是等比数列;
(2)若
,
,
成等差数列,记
,数列
的前n项和为
,求证:
.
![](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/871efdbd31a7c8886a3970447fe749dc.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc17ca3ab612ea9cf6cfa1eea53cb1eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2694813e9fe254366e041221c81ba504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1341feb191e5db2ff020502ca1c216b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f2a36a909d0e9f0eb3a9281eb6213d.png)
您最近一年使用:0次
10 . 已知数列
的首项
,
是
与
的等差中项.
(1)求证:数列
是等比数列;
(2)证明:
.
![](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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fa65c121c7b361e141deaeee7a1d67.png)
您最近一年使用:0次
2023-10-30更新
|
1947次组卷
|
9卷引用:黑龙江省百师联盟2024届高三一轮复习联考(二)数学试题
黑龙江省百师联盟2024届高三一轮复习联考(二)数学试题甘肃省部分校2024届高三上学期10月质量检测数学试题(已下线)模块四 专题6 大题分类练(数列)基础夯实练(人教A)四川省宜宾市南溪第一中学校2024届高三上学期一诊考试理科数学模拟试题(已下线)第二篇 “搞定”解答题前3个 专题2 数列解答题【练】高三逆袭之路突破90分黑龙江省佳木斯市三校联考2024届高三上学期第三次调研考试数学试题(已下线)专题10 数列不等式的放缩问题 (7大核心考点)(讲义)(已下线)黄金卷08(已下线)题型18 4类数列综合