名校
解题方法
1 . 数列
,
,
(
)
(1)是否存在常数
,使得数列
是等比数列,若存在,求出
的值若不存在,说明理由;
(2)设
,证明:当
时,
.
![](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/483bf3858e5dcdb2bcd2532d232aabda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
(1)是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec6fb9e0625b85be3103d317fbb0cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1761de3795504d0ec416973430e3458d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec6fb9e0625b85be3103d317fbb0cca.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6308c1c4ae22bd1e02470e067c376e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0215573641a657fdf1aa67edb4faba2.png)
您最近一年使用:0次
2 . 已知数列
满足
,且
.
(Ⅰ)求
,
的值;
(Ⅱ)是否存在实数
,
,使得
,对任意正整数
恒成立?若存在,求出实数
、
的值并证明你的结论;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a61e435e639c6491603a5e94b3a17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(Ⅱ)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14240403dc63352209dc8e0eb28d6ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2019-07-11更新
|
413次组卷
|
2卷引用:江苏省无锡市普通高中2018-2019学年高二下学期期末数学(理)试题
名校
3 . 已知数列
和
,其中
,当
时,试比较
与
的大小,并用数学归纳法证明你的结论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1ce1d77a0a00432fccf2a0b3b85dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea0dab63dac92bedf9fd37c3e80c076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
您最近一年使用:0次
名校
4 . 正项数列{an}的前n项和为Sn,且
对于任意的n∈N*均为成立.
(1)求a1,a2,a3;
(2)猜想数列{an}的通项公式并证明;
(3)比较
与
的大小并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ab359f97b46f33828f20d06b65b26e.png)
(1)求a1,a2,a3;
(2)猜想数列{an}的通项公式并证明;
(3)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e578f650290b29627cdb1402c945cfcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2d2ba6c5ad2b2d548b39855a36c98b.png)
您最近一年使用:0次
名校
5 . 已知
为等差数列,
为等比数列,公比为q(q≠1).令A=
.A={1,2},
(1)当
,求数列
的通项公式;
(2)设
,q>0,试比较
与
(n≥3)的大小?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2448cf72af76b810310e4cfb9818e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee217b7825a7393aa2adb0339f6954c9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e62e0fac816004f761126bb4b4b789d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2448cf72af76b810310e4cfb9818e2e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc49fb6f3d806949ad10b7826b0969a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfccafa83afe5ee21eab6ef2b2c8852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cba31e8c939286cafff96e8d715a697.png)
您最近一年使用:0次
2019-01-15更新
|
508次组卷
|
2卷引用:江苏省无锡市锡山高级中学实验学校2019届高三12月月考数学试题
解题方法
6 . 将正整数排成如图的三角形数阵,记第
行的
个数之和为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/92541fd2-b8bb-42dc-800a-3e970369a24b.png?resizew=138)
(1)设
,计算
,
,
的值,并猜想
的表达式;
(2)用数学归纳法证明(1)的猜想.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/92541fd2-b8bb-42dc-800a-3e970369a24b.png?resizew=138)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b9fcf130e912aa06320d82793b65e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)用数学归纳法证明(1)的猜想.
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解题方法
7 . 已知数列
的前n项和为
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016c31f6fd165bc81a76956da545029f.png)
,令
.
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf21791a47151bfee683e95ffee1bdcf.png)
,用数学归纳法证明
是18的倍数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016c31f6fd165bc81a76956da545029f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d5fa85887816de29bcff4f143e3f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f32322ce51946bd1078748378816c7.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf21791a47151bfee683e95ffee1bdcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d5fa85887816de29bcff4f143e3f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
您最近一年使用:0次
2014高三·全国·专题练习
真题
解题方法
8 . 已知数列{bn}是等差数列,b1=1,b1+b2+…+b10=145.
(1)求数列{bn}的通项公式bn;
(2)设数列{an}的通项an=loga
(其中a>0且a≠1).记Sn是数列{an}的前n项和,试比较Sn与
logabn+1的大小,并证明你的结论.
(1)求数列{bn}的通项公式bn;
(2)设数列{an}的通项an=loga
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322879f2a9603a5d124844f5eea796a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
您最近一年使用:0次
2016-12-02更新
|
1301次组卷
|
5卷引用:【全国校级联考】江苏省无锡市江阴四校2017-2018学年高二下学期期中考试数学(理)试题
【全国校级联考】江苏省无锡市江阴四校2017-2018学年高二下学期期中考试数学(理)试题(已下线)2014届高考数学总复习考点引领+技巧点拨第七章第3课时练习卷专题11.4 数学归纳法(练)-江苏版《2020年高考一轮复习讲练测》1998年普通高等学校招生考试数学(理)试题(全国卷)1998年普通高等学校招生考试数学(文)试题(全国卷)