10-11高二下·安徽亳州·期末
1 . 在数列
中,
,且前
项的算术平均数等于第
项的
倍
.
(1)写出此数列的前
项;
(2)归纳猜想
的通项公式,并用数学归纳法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](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/e87670af2d245aaff0dbeef2c56d0ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d292dde9fb0b3ab8259082569876a8.png)
(1)写出此数列的前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
(2)归纳猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
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9-10高二下·重庆·期末
名校
解题方法
2 . 已知
满足
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8437810c6f2c7a92470d0f12738da100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36d97df9893eec87425279131f8c31c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f92db8bf38b88201bf2f156467d5a2.png)
(1)求,并猜想
的表达式;
(2)用数学归纳法证明对的猜想.
您最近一年使用:0次
2016-12-01更新
|
1439次组卷
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6卷引用:安徽省淮北市濉溪县2018-2019学年高二下学期期末数学(理)试题
安徽省淮北市濉溪县2018-2019学年高二下学期期末数学(理)试题(已下线)2010年重庆一中高二下学期期末考试数学(理)试题(已下线)2010年山东省东明县第一高级中学高二下学期期末考试理科数学卷2017届山东潍坊中学高三上学期开学考试数学(理)试卷湖北省武汉外国语学校2016-2017学年高二下学期期中考试数学(理)试题河南省洛阳市第一高级中学2019-2020学年高二5月月考数学(理)试题
11-12高二下·安徽宿州·期中
3 . 用数学归纳法证明
(
)时,从“
到
”左边需增乘的代数式为
![](https://img.xkw.com/dksih/QBM/2014/6/16/1571775569362944/1571775574810624/STEM/0edc9c3042834ab1a8c8ac3a2bd90f0e.png)
![](https://img.xkw.com/dksih/QBM/2014/6/16/1571775569362944/1571775574810624/STEM/c1047b78d1504a43a498fbc8a4edfff6.png)
![](https://img.xkw.com/dksih/QBM/2014/6/16/1571775569362944/1571775574810624/STEM/f8d95859e4c34df0b078e6dac4aa1f05.png)
![](https://img.xkw.com/dksih/QBM/2014/6/16/1571775569362944/1571775574810624/STEM/d3137a936b744bbc940b7576d6b99dc9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2016-12-01更新
|
904次组卷
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6卷引用:2011-2012学年安徽省宿州市高二下学期期中质量检测理科数学试卷
(已下线)2011-2012学年安徽省宿州市高二下学期期中质量检测理科数学试卷(已下线)2011-2012学年山东省济宁市梁山一中高二下学期期中理科数学试卷(已下线)2011—2012学年甘肃省张掖二中高二下学期期中理科数学试卷(已下线)2013-2014学年湖北省部分重点中学高二下学期期中考试理科数学试卷2015-2016学年江西省宜春市奉新一中高二下第一次月考理科数学试卷(已下线)专题6.6 数学归纳法 (练)-浙江版《2020年高考一轮复习讲练测》
11-12高三·安徽宿州·阶段练习
解题方法
4 . 已知数列
的前
项和
与
满足
,其中
是与
无关的常数,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e7bffaae768907ed8edf87fe2cd785.png)
(1)求
;
(2)求
和
的关系式;
(3)猜想用
和
表示
的表达式(须化简),并证明之.
![](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/e77e55e18edbadc764c3885916703a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e7bffaae768907ed8edf87fe2cd785.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7230de53663c75658c58bbf206a0085.png)
(3)猜想用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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10-11高二下·安徽马鞍山·期中
名校
解题方法
5 . 当
时,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbda586766d3e014574f48455f076825.png)
(Ⅰ)求
,
,
,
;
(Ⅱ)猜想
与
的关系,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16f86e49d19478992441292c6528582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbda586766d3e014574f48455f076825.png)
(Ⅰ)求
![](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/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
(Ⅱ)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2016-12-01更新
|
1217次组卷
|
12卷引用:2010-2011年安徽省马鞍山市第二中学高二下学期期中考试理科数学
(已下线)2010-2011年安徽省马鞍山市第二中学高二下学期期中考试理科数学(已下线)2011-2012学年陕西省师大附中高二上学期期末考试理科数学(已下线)2011-2012学年广东省新兴县惠能中学高二下学期第一次月考理科数学试卷(已下线)2011-2012学年山东省日照一中高二下学期模块考试理科数学试卷(已下线)2011-2012学年山东冠县武训高中高二下学期模块考试理科数学试卷(已下线)2011—2012学年福建师大附中高二下学期期中理科数学试卷(已下线)2012-2013学年浙江台州书生中学高二下学期第一次月考理科数学试卷2014-2015学年山东省沂源县一中高二下学期阶段性检测理科数学试卷山西省祁县中学2017-2018学年高二4月月考数学(理)试题【市级联考】湖南省张家界市2018-2019学年高二第一学期期末联考理科数学试题陕西省商洛市洛南县2018-2019学年高二下学期期中数学(理)试题河南省郑州市巩义中学2019-2020学年高二下学期期中考试数学(理)试题
6 . 已知函数
,数列
满足递推关系式:
(
),且
.
(Ⅰ)求
、
、
的值;
(Ⅱ)用数学归纳法证明:当
时,
;
(Ⅲ)证明:当
时,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b92cc818d0fb0eb7999deaa03f780fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e7fa864d15504b352699a941b39430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381576e698a46df8c497e6b5f8346ddc.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb5ca241bb7c313ef0366d3ddba93bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbeed5324c432101be517dd6f5c735b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d199f9235e3bd36bfa78c3772e941896.png)
(Ⅱ)用数学归纳法证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9340682e974d0f66fffa056d023079d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc8d9edcad32ed464c44b58b9ea662d.png)
(Ⅲ)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9340682e974d0f66fffa056d023079d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209433be5b0eb7112a4fadd32de1aecc.png)
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11-12高三上·安徽蚌埠·阶段练习
7 . 已知函数
,函数
的图象与
的图象关于点
中心对称.
(1)求函数
的解析式;
(2)如果
,
,试求出使
成立的
取值范围;
(3)是否存在区间
,使
对于区间内的任意实数
,只要
且
时,都有
恒成立?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9261dcb08aba06d24e331d5049f0bb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d655ee6d4c2285b6f59652360862d2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe46513221da1b16ffe497a825b0e53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041809b54951a7d2e480eb6b37e7c546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8aa839dcd6fcfad871dd2e67d2e8ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)是否存在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f2ac7d62be1c5f4c65435585a6ae6b.png)
![](https://img.xkw.com/dksih/QBM/2011/12/22/1570628645380096/1570628650975232/STEM/2fb8da5ce6a141988bb149524b791a6a.png?resizew=13)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d4e4e1775e319b6a740ec72ea8bc6b.png)
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真题
8 . 首项为正数的数列{
}满足
.
(Ⅰ)证明:若
为奇数,则对一切
,
都是奇数;
(Ⅱ)若对一切
,都有
,求
的取值范围.
![](https://img.xkw.com/dksih/QBM/2010/3/29/1569681460748288/1569681643634688/STEM/61d2ae4434e5498d832f074ba4e8d49c.png)
![](https://img.xkw.com/dksih/QBM/2010/3/29/1569681460748288/1569681643634688/STEM/58cffe4cae914952b29642938c8eb213.png)
(Ⅰ)证明:若
![](https://img.xkw.com/dksih/QBM/2010/3/29/1569681460748288/1569681643634688/STEM/cceac36296b440e09ab596d7f37d512f.png)
![](https://img.xkw.com/dksih/QBM/2010/3/29/1569681460748288/1569681643634688/STEM/c053505755e7471e8b674e28e9c044a8.png)
![](https://img.xkw.com/dksih/QBM/2010/3/29/1569681460748288/1569681643634688/STEM/61d2ae4434e5498d832f074ba4e8d49c.png)
(Ⅱ)若对一切
![](https://img.xkw.com/dksih/QBM/2010/3/29/1569681460748288/1569681643634688/STEM/f8bf962207ba43f39aa745555b66dec5.png)
![](https://img.xkw.com/dksih/QBM/2010/3/29/1569681460748288/1569681643634688/STEM/dfab924a63134323bebeb1d8876f7ff6.png)
![](https://img.xkw.com/dksih/QBM/2010/3/29/1569681460748288/1569681643634688/STEM/cceac36296b440e09ab596d7f37d512f.png)
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