1 . 正项数列
满足
.
(1)求
;
(2)猜想数列
的通项公式,并给予证明;
(3)若
,求证:
是无理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624f10fb877734018a18b280e4efa7ba.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
(2)猜想数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ccfa38896c6ac193fbab372f963dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
您最近一年使用:0次
10-11高二·江苏·期中
2 . 已知数列
满足
,且
.
(1)求
,
,
;
(2)由(1)猜想
的通项公式
;
(3)用数学归纳法证明(2)的结果.
![](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/1072b52c1d72b5d383cdaeb24fa2b102.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)
(2)由(1)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)用数学归纳法证明(2)的结果.
您最近一年使用:0次
2022-03-01更新
|
638次组卷
|
4卷引用:江苏省连云港市锦屏高级中学2017-2018学年高二下学期期中数学(理)试题
江苏省连云港市锦屏高级中学2017-2018学年高二下学期期中数学(理)试题(已下线)2010-2011学年江苏省溱潼中学高二年级期中数学(理)试卷(一)(已下线)4.4 数学归纳法2苏教版(2019)选择性必修第一册课本习题 习题4.4
3 . 用“数学归纳法”证明:
能被
整除.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e924cfec45386bf71c518e5aab0894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39241f2eeccaa16d0550d851619bcb42.png)
您最近一年使用:0次
13-14高二下·江苏连云港·期末
4 . 观察下列不等式:
,
,
,
,
……
(1)由上述不等式,归纳出一个与正整数
有关的一般性结论;
(2)用数学归纳法证明你得到的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce48dc63b6d4bbb3289a0f3df2b0f3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff75682768ce7ae1abb36b2a90d6267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b884959dbcf9a192f09739eec47676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a23c6be201b253ee0c229f2cd54482.png)
……
(1)由上述不等式,归纳出一个与正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac19e2a797cd0a408316988a63b3755.png)
(2)用数学归纳法证明你得到的结论.
您最近一年使用:0次