题目
题型:不详难度:来源:
把正整数按从小到大顺序排列成下列数表,数表中第
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065926-32936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065926-39988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065926-95719.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065926-77758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065926-32936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065927-19483.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065927-54260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065927-88252.png)
(2)记
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065927-87583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065928-98135.png)
(3)猜想
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065928-78954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065928-38954.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065928-11518.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-75656.png)
(3)猜想:当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-60462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-27485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-84775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-28212.png)
证明:(法一)二项式定理的应用
(法二)数学归纳法
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-27880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-73285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-86846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-43037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065931-60524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065931-55136.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065931-68271.png)
第二问中,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065931-47209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065932-74704.png)
第三问中,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065932-67395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065932-87925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065932-96181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065933-41186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065933-20199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065933-29118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065933-71175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065934-15919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065934-96876.png)
猜想:当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-60462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-27485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-84775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-28212.png)
解:(1)到第
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-27880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065934-80659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-86846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-43037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065931-60524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065931-55136.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065931-68271.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065931-47209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065932-74704.png)
由叠加可得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-75656.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065934-60180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065932-87925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065932-96181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065933-41186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065933-20199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065933-29118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065933-71175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065934-15919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065934-96876.png)
猜想:当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-60462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-27485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065929-84775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065930-28212.png)
证明:(法一)二项式定理的应用 (6分)
(法二)数学归纳法
核心考点
试题【(本题满分15分)把正整数按从小到大顺序排列成下列数表,数表中第行共有个正整数:设是位于数表中从上往下数第行、从左往右数第个数(1)若,求的值;(2)记,求数列】;主要考察你对合情推理与演译推理等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065917-20657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065917-55109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065917-81523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065918-41165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065918-41165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065917-55109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065918-45468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065918-53000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065918-37550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065918-66807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065917-55109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065919-60293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065919-38686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065919-38686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065917-55109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065919-73843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065919-33472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065914-73659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065906-75113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065906-80680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065906-75113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065906-52038.png)
有如下运算和结论:①
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065906-53537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065907-16773.png)
数列;③数列
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065907-86153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065907-21910.png)
存在正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065907-78954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065908-21068.png)
为正确的结论序号都填上)
A.由数列![]() ![]() |
B.平面内不共线的三点确定一个圆,由此猜想空间不共面的三点确定一个球 |
C.垂直于同一平面的两条直线平行,又直线![]() ![]() ![]() |
D.由![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065851-69783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065852-54597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065852-34889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065852-14822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065852-83148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106065853-16385.png)
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
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