解题方法
1 . 已知数列
的前n项和为
,
,
.
(1)求
,并证明数列
是等比数列;
(2)若
,求数列
的前n项和
.
![](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/00fa4a3584fc553ea72b1395e87f1aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca9db70d3baaab9aa92255f71251506.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f543f3aafa4740bd65aefc8d8de4b6f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad8abce67ab1613db8bf36fdfaf35a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
2 . 已知数列
满足
,
,且
,
.
(1)证明:数列
为等差数列;
(2)记数列
的前n项和为
,求数列
的通项公式,并求出使得不等式
成立的n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20616e3d8fc3aea730b3eefeef902b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf584ab870ec1990971ce332b74ddbb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65c44af8125cfd1e8c9a6d2985bcee6.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(2)记数列
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa06f906c8f9b48407cc1c52f9629cc6.png)
您最近一年使用:0次
2023高三·全国·专题练习
3 . 已知数列
的前n项和是
,且
.
(1)证明:
为等比数列;
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a5bcdb7e6d6818254e00d02645e271.png)
(3)
为数列
的前n项和,设
,是否存在正整数m,k,使
成立,若存在,求出m,k;若不存在,说明理由.
![](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/e3c07d6d0c63061e09e36b5a2c74760b.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a5bcdb7e6d6818254e00d02645e271.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878b4bc8b23c9f486874016f32221333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59fe8864b6c25590de9d542f54b9422.png)
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22-23高二下·江西·阶段练习
名校
解题方法
4 . 已知数列
满足
,且
.
(1)证明:数列
是等比数列,并求出
的通项公式.
(2)设
,数列
的前
项和为
,若不等式
对任意的
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/51ef1a9fe92efa3ae54e821ecf7a99c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe49088cdaf4bfb36acb0cb5bc4104c7.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1052aee3d6061385b17559f4677a8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634683b24b1de0436d90a67fc52b4f24.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b63b8c3a2405d50ab29c425fdfdf8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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5 . 数列
满足
,
.
(1)求数列
的通项公式;
(2)记
,数列
的前
项和为
,求使
成立的最小正整数
.
![](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/4a9fdad6fde58bb53b02a81687cf74f2.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e107122a7fd25795ea6719d5d4f414e.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1745a7e31d054962fa2331fda652a43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2023-05-21更新
|
373次组卷
|
3卷引用:江西省宁冈中学2022-2023学年高二下学期6月期末数学试题
解题方法
6 . 已知数列
中,
,且
.
(1)求
,并证明
是等比数列;
(2)求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2219ea8d05ddac5cc049b09e602ccb6a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483eb4433fee05a5810a276433b1742.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
名校
解题方法
7 . 已知数列
满足
,且
.
(1)求证数列
是等比数列,并求
的通项公式;
(2)若
对任意的
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d57847d7809d0590b5d1d8756b91e7f.png)
(1)求证数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f0bd98fc78c7f7a2e0d26ffe1a093f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812da0799f5731236918692a5cc707ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28652e52c0b02a343e618935ea625cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-03-28更新
|
478次组卷
|
3卷引用:江西省南昌市雷式中学2022-2023学年高二下学期3月月考数学试题
8 . 在一个有穷数列的每相邻两项之间插入这两项的和,形成新的数列,我们把这样的操作称为该数列的一次“和扩充”.如数列1,2第1次“和扩充”后得到数列1,3,2,第2次“和扩充”后得到数列1,4,3,5,2.设数列a,b,c经过第n次“和扩充”后所得数列的项数记为
,所有项的和记为
.
(1)若
,求
,
;
(2)设满足
的n的最小值为
,求
及
(其中[x]是指不超过x的最大整数,如
,
);
(3)是否存在实数a,b,c,使得数列{
}为等比数列?若存在,求
b,c满足的条件;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb179b52814cf68ce86201e14c1dcae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)设满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d9ec2496e67711ab849b0f8988cd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28ede5e4c703019a7250cb63503df94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe1e778c9e668594c42b77459328c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf031d0c50f5013e0a8469d1f609d81.png)
(3)是否存在实数a,b,c,使得数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9fbbd9c88736e500f5251f97b08452.png)
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2023-03-28更新
|
566次组卷
|
6卷引用:江西省赣州市南康区唐江中学2022-2023学年高二下学期期中数学试题
解题方法
9 . 已知数列
满足
,
.
(1)证明:数列
是等比数列;
(2)设
,求数列
的前n项和
.
![](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/3998df04d0a8ded946c3f39d545fdc7e.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3b9192a77a75259650dea7a93fef415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-03-16更新
|
1301次组卷
|
4卷引用:江西省宜春市丰城市东煌学校2022-2023学年高二下学期6月月考数学试题
江西省宜春市丰城市东煌学校2022-2023学年高二下学期6月月考数学试题(已下线)专题06 数列在高考中的考法(难点,十一大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)四川省巴中市2023届高三“一诊”考试数学(文)试题(已下线)专题11数列(解答题)
名校
解题方法
10 . 数列
的前n项和为
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705706239ba64bc02d062b54f0e20b60.png)
.
(1)求
;
(2)求数列
的通项公式
;
(3)求
的和
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705706239ba64bc02d062b54f0e20b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2889dd3096379db5dfdd51305bdbb743.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed529240a883f68f0921e818addeb9c8.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b3234e3d63a01d2b4f2282ced7edb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2023-06-20更新
|
399次组卷
|
2卷引用:江西省吉安市宁冈中学2023-2024学年高二上学期期末模拟数学试题