解题方法
1 . 已知数列
的前n项和为
,
.
(Ⅰ)求数列
的通项公式;
(Ⅱ)设数列
的前n项和为
,点
在直线
上,若存在
,使不等式
成立,求实数
的最大值.
![](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/c8370a173854471a3eb27637993a3d5d.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d949ab822208c9c63a85b533489fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c609ffa4e2bc842242fec0384c409e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c11bdfc75b793d660afb68b14b15932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28652e52c0b02a343e618935ea625cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d5f0b443aa1062359061a69e1c2fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2 . 设数列
的前n项和为
.已知
.
(Ⅰ)求
的通项公式;
(Ⅱ)若数列
满足
,求
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a9ec979c0f3b2be12cab17ebdbc76a.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(Ⅱ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a25a91092a09b93b0e3a2c23d8ea728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2016-12-03更新
|
10062次组卷
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28卷引用:2015年全国普通高等学校招生统一考试理科数学(山东卷)
2015年全国普通高等学校招生统一考试理科数学(山东卷)山东济南市历城第二中学2020-2021学年高二下学期开学考试数学试题山东省淄博市高青县第一中学2023-2024学年高二下学期期中学分认定考试数学试题2015-2016学年河北省正定中学高二上期中数学试卷2015-2016学年河南省许昌市四校高二上学期期末理科数学试卷2015-2016学年河南省许昌市四校高二上学期期末文科数学试卷2016-2017学年河北鸡泽县一中高二上学期期中数学试卷浙江省宁波市北仑中学2016-2017学年高一下学期期中考试数学试题2018届高三数学训练题(42):高考大题突破练--数列 (已下线)二轮复习测试专项 【新课标版理科数学】专题四 数列与不等式(已下线)二轮复习测试专项 【新课标版文科数学】专题四 数列与不等式高中数学人教A版必修5 第二章 2.5.1 等比数列的前n项和(1)(已下线)实战演练5.2-2018年高考艺考步步高系列数学【全国百强校】陕西省西安市第一中学2018-2019学年高二10月月考数学试题2020届天津市南开中学高三上学期数学统练(5)试题2019届湖南省长沙市雅礼中学高三上学期入学考试数学(理)试题2020届广西钦州市第三中学高三上学期理数考试题(已下线)专题04 求数列的通项公式(第二篇)-备战2020年高考数学大题精做之解答题题型全覆盖沪教版(上海) 高三年级 新高考辅导与训练 第二部分 走近高考 第四章 数列与数学归纳法高考题选上海市进才中学2019-2020学年高一下学期期末数学试题江苏省徐州市丰县华山中学2020-2021学年高二上学期9月月考数学试题陕西省咸阳市高新一中2020-2021学年高三上学期第三次质量检测数学(理)试题吉林省吉林市吉林第一中学2020-2021学年高二上学期阶段性考试数学试题陕西省咸阳市高新一中2020-2021学年高三上学期第五次质量检测理科数学试题(已下线)专题十 分组求和法求数列的前n项和-2020-2021学年高中数学专题题型精讲精练(2019人教B版选择性必修第三册)浙江省金华市磐安县第二中学2019-2020学年高一下学期返校考试数学试题(已下线)专题21 数列解答题(理科)-2专题28数列解答题
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3 . 已知数列
是首项为正数的等差数列,数列
的前
项和为
.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef5561a645f3f67290f31631d465fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958b23fabde33988b941240a6f82c44b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802fe1d43065964fd79c25932f3bc13b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4464b3b4eb6e52ee02f095aae84f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb26cd1601fe7e76e1e2dc0b4909324a.png)
您最近一年使用:0次
2016-12-03更新
|
9446次组卷
|
24卷引用:2015年全国普通高等学校招生统一考试文科数学(山东卷)
2015年全国普通高等学校招生统一考试文科数学(山东卷)2016届辽宁省大连市二十中高三10月月考文科数学试卷2017届河北沧州一中高三11月月考数学(文)试卷黑龙江省牡丹江市第一高级中学2018届高三10月月考数学(文)试题【全国校级联考】云南省红河州2018届高三复习统一检测数学(理)试题黑龙江省哈尔滨市第六中学2020届高三上学期期中数学(文)试题河南省濮阳市2019-2020学年高二上学期期末数学(理)试题河南省濮阳市2019-2020学年高二上学期期末数学(文)试题陕西省榆林市绥德中学2019-2020学年高二下学期第一次阶段性测试数学(文)试题江西省宜春市奉新县第一中学2019-2020学年高一下学期第一次月考数学试题安徽省安庆市怀宁中学2019-2020学年高一下学期期中理科数学试题江西省靖安中学2019-2020学年高一下学期第一次月考数学试题山西省新绛县第二中学2019-2020学年高一下学期6月月考数学试题人教A版(2019) 选择性必修第二册 过关斩将 全书综合测评安徽省安庆市怀宁县第二中学2020-2021学年高三上学期第五次月考数学(文)试题河南省焦作市县级重点中学2021-2022学年高三上学期期中考试文科数学试题甘肃省兰州市第五十九中学2022-2023学年高二下学期开学检测数学试题黑龙江省哈尔滨市第十三中学2022-2023学年高三下学期开学检测数学试题内蒙古包头市第四中学2022届高三第四次校内模拟文科数学试题甘肃省张掖市某重点校2023-2024学年高二上学期10月月考数学试题湖南省长沙市雅礼中学2024届高三上学期月考试卷 (三)数学试题湖南省长沙市雅礼中学2024届高三上学期月考试卷(三)(已下线)专题21 数列解答题(文科)-2专题29数列解答题
4 . 已知等差数列
满足:
,
,该数列的前三项分别加上
后顺次成为等比数列
的前三项
(1)分别求数列
,
的通项公式
,
;
(2)设
若
恒成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f3ea1398d6f0cdcbb070c657c9791a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a703ff11405244792c560472fe439d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)分别求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008a2e7b7916905ddf425d20623f2eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9309860ccff4b2cce7e9437e8fff7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
您最近一年使用:0次
5 . 已知数列
是各项均为正数的等差数列,首项
,其前
项和为
,数列
是等比数列,首项
,且
.
(1)求数列
和
的通项公式;
(2)令
,其中
,求数列
的前
项和
.
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/5cfb5bbec3e241d4a1efdce3c8c4acd4.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/0114191ca3d1420898f1490c1070b954.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/f8435f2fe2f2499ebfea37ed17c22c9b.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/5dd16405c374409bac36cc67988591ff.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/1432f17247dc4b95b357d8c6b88b3008.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/729c4cd35c624af485b0f51a30a14aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fe4c330106d73c90d32865369e8538.png)
(1)求数列
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/5cfb5bbec3e241d4a1efdce3c8c4acd4.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/1432f17247dc4b95b357d8c6b88b3008.png)
(2)令
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/5586a4d7264d4d4e91c1a49b5d067225.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/e29445b364714577b57497f6e2bc9cca.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/2d12f79a83fb499080a921f3b770090a.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/58aee374dcc3474a8fb2974e8ba34614.png)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572105349791744/1572105355862016/STEM/4e492a4421b04e4a81576e3e4e003587.png)
您最近一年使用:0次
2016-12-03更新
|
533次组卷
|
2卷引用:2015届山东省文登市高三第二次模拟考试理科数学试卷
解题方法
6 . 已知数列
的前
项和为
,
、
满足
(
为常数,
且
).
(1)求数列
的通项公式;
(2)设
,当
时,求数列
的前
项和
.
![](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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4916047ebb0abf8822412a4e163084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a369ce3949b2bd2747a48054f7b951c4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accc88c0f186efc0b15dce88dbf10e53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19215074e16c7288e853d336897bead.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
解题方法
7 . 已知数列
是等比数列,首项
,公比
,其前
项和为
,且
,
,
成等差数列.
(1)求数列
的通项公式;
(2)若数列
满足
,
为数列
的前
项和,若
恒成立,求
的最大值.
![](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/f71acdb04454c77e1e25ad4f336cccfe.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/90bce834ac8aaa642b8fb73991c1c426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c40980226328591a49bf85b56b9562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28cf1b08721d77f427f8c11558cacdf.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d281511eee5f8f440bb14cc04e34331f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8a65af0ed8684edc5c6489ff1d263e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-03更新
|
784次组卷
|
2卷引用:2015届山东省文登市高三第二次统考理科数学试卷
8 . 已知数列
的前
项和
,满足
为常数,且
,且
是
与
的等差中项.
(Ⅰ)求
的通项公式;
(Ⅱ)设
,求数列
的前
项和
.
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/1ac07b8336584c8da0d03b01f5758954.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/4bccc64b98a24d01b9a8e79bd78e97d2.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/5691b53f7f7746e4a1b5e29718a95606.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/965ece555ce140e9ab4443149f9f8b7d.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/8d4106bff10c4f9481d9fb96adbdac10.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/247cfba8ccce40e99e04b6bb7ba0066c.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/e2afb42b54eb4da8b0ca5e45827cc736.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/0c2394ffd77749738ff2be23c6408805.png)
(Ⅰ)求
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/1ac07b8336584c8da0d03b01f5758954.png)
(Ⅱ)设
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/2e3e09507e114b9ba10eb69f73ab3bd4.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/d78492b247bd42faae64718d365a7fad.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/4bccc64b98a24d01b9a8e79bd78e97d2.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572065347182592/1572065353146368/STEM/4b5155912289413e9fe8a3373f16308c.png)
您最近一年使用:0次
解题方法
9 . 已知
是等差数列
的前n项和,数列
是等比数列,
,
恰为
的等比中项,圆
,直线
,对任意
,直线
都与圆C相切.
(I)求数列
,
的通项公式;
(II)若对任意
,
,求
的前n项和
的值.
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a24e6bcf49b8e45531a2d4e4c70c181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceda82fbc56d664a5d8b8c9e8de1fd18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e310e2f7d9ae5290cbddb869938b912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965d0c1c66ec43e48c36d93f705f9ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4330ab95101b08e18ff935fd7e78a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(I)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(II)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac07953530e3c248b3438fb200fb1661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
解题方法
10 . 已知
为等比数列,其中
,且
成等差数列.
(1)求数列
的通项公式;
(2)设
,求数列
的前
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/206cce32fab24a9a7ba2d1cba8543826.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df1e8c28789ee186157ec527a7f5199.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2016-12-03更新
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5卷引用:【全国百强校】山东省济南市历城第二中学2019接高三11月月考数学(理)试题
【全国百强校】山东省济南市历城第二中学2019接高三11月月考数学(理)试题山东省济南市历城第二中学2019届高三11月调研检测数学(理)试题2015届四川省新津中学高三一诊模拟理科数学试卷2015-2016学年河北省邯郸市魏一中等校高二上学期期中文科数学试卷(已下线)2018年12月28日 《每日一题》(理数)人教必修5+选修2-1(高二上期末复习)-数列求和的常用方法