已知数列
满足
,前n项和
.
(1)求
,
,
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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4471e05dc80d3cc7bd8a37cf26a95ecf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)用数学归纳法证明(1)的猜想.
21-22高二下·江西赣州·期中 查看更多[2]
更新时间:2022-04-22 14:39:05
|
相似题推荐
解答题-证明题
|
适中
(0.65)
【推荐1】给出下面的数表序列:
其中表
有
行,第1行的
个数是1,3,5,…,
,从第2行起,每行中的每个数都等于它肩上的两数之和.
(1)写出表4,验证表4各行中数的平均数按从上到下的顺序构成等比数列,并将结论推广到表
(不要求证明)
(2)每个数表中最后一行都只有一个数,它们构成数列1,4,12,…,记此数列为
,求数列
的前
项和
表1 | 表2 | 表3 | … |
1 | 1 3 | 1 3 5 | |
4 | 4 8 | ||
12 |
其中表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c9720d6e378b2b2b33cad6dc2144a1f.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/627a57cd9fdb1f586f35d9825b6bcc0b.png)
(1)写出表4,验证表4各行中数的平均数按从上到下的顺序构成等比数列,并将结论推广到表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
(2)每个数表中最后一行都只有一个数,它们构成数列1,4,12,…,记此数列为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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适中
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真题
【推荐2】已知数列
、
、
、
,其中
、
、
、
是首项为
,公差为
的等差数列;
、
、
、
是公差为
的等差数列;
、
、
、
是公差为
的等差数列
.
(1)若
,求
;
(2)试写出
关于
的关系式,并求
的取值范围;
(3)续写已知数列,使得
、
、
、
是公差为
的等差数列,
,依次类推,把已知数列推广为无穷数列.提出同(2)类似的问题(2)应当作为特例),并进行研究,你能得到什么样的结论?
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef367814f1a7f44e4920f9f55daea063.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e84c30444f13d37ada78285dc4f83b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066bed69d03aee63a37e1259f6599e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066bed69d03aee63a37e1259f6599e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc29ee719feeedfbc8c529cf11348abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef367814f1a7f44e4920f9f55daea063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd180baa7212528480ce32f2fda8960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6244222d8b4e21fc28c0454d0276a1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27942f056fca5c337e75d2e9b28ad547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)试写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef367814f1a7f44e4920f9f55daea063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef367814f1a7f44e4920f9f55daea063.png)
(3)续写已知数列,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef367814f1a7f44e4920f9f55daea063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a555e932cee7a505419ca454e4d1a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb38c0f6faeb81092f6039beab4a525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8fa7e4ccfc0eee96ee1d2ba8fd4c9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
您最近一年使用:0次
解答题-证明题
|
适中
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解题方法
【推荐2】已知等差数列
的首项为
,公差为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
,前
项和为
.
(1)若对
,
为常数k,求k;
(2)若
,用数学归纳法证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0432d8460941037411ded150b3959339.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f282b34cb12ceb853401ede8b9ff7408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a3dab80709d7a4798633a904e1323d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7335c79ec0592fc36288f5135e86c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0432d8460941037411ded150b3959339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132e9579e58d8d5225e2340e1f43adf1.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐1】对任意正整数n,设
表示n的所有正因数中最大奇数与最小奇数的等差中项,
表示数列
的前n项和.
(1)求
,
,
,
,
的值;
(2)是否存在常数s,t,使得
对一切
且
恒成立?若存在,求出s,t的值,并用数学归纳法证明;若不存在,请说明理由.
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求
![](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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(2)是否存在常数s,t,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90945bcc1478641d7077ad793871f4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
您最近一年使用:0次
解答题-问答题
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适中
(0.65)
解题方法
【推荐2】已知数列
满足
.
(1)求
;
(2)猜想数列通项公式
,并用数学归纳法给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f700a2f34e8799df971f6f1680080b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed529240a883f68f0921e818addeb9c8.png)
(2)猜想数列通项公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
解答题-问答题
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适中
(0.65)
解题方法
【推荐1】已知数列
的通项公式为
,数列
的前
项和为
.
(1)求数列
的通项公式;
(2)设
,问是否存在正整数
,使得
成立,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f1157a16ac2ab5d4ff31ed051955b2.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/84bdd7639d74c31680ddaef489ba9bfe.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b67af73f586837594ab0db4b89baed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80efea44d0b7f278557c7f0f73b8bda8.png)
您最近一年使用:0次
解答题-问答题
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解题方法
【推荐2】已知等差数列
的前
项和为
,且
,
,数列
满足
,
.
(1)求数列
和
的通项公式;
(2)设
,数列
的前
项和为
,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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73abda0b2c65194421a02d6dc1380f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3931e6266decbab4ab76b280f61bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34238266862aad17d484e065e9e7d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031d7a1572765b0dacbfdbaf131c449b.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5608d0c8d3b5b997012cb6dc698d9f4.png)
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