题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054529-31098.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054529-45020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054529-27964.gif)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-93617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-67876.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-40407.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-21171.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-60878.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-24953.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-13665.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-46094.gif)
答案
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-11072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-93272.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054529-31098.gif)
(1)(ⅰ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-93617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054529-45020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054532-25882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-67876.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054532-63172.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054532-71425.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-67876.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054532-94595.gif)
…………………………5分
(ⅱ)由于
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-67876.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054532-94595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-67876.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054533-17915.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054529-45020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054533-67865.gif)
先用数学归纳法证明下面的不等式成立:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054533-36337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054533-94398.gif)
Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054533-97680.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054534-62713.gif)
Ⅱ)假设结论对
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054534-64633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054534-38922.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054534-84512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054535-33728.gif)
综合Ⅰ),Ⅱ)可知,不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054533-36337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054533-94398.gif)
因此,当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054533-94398.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054535-13689.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054535-10734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054535-95137.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054535-31734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054536-31832.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-21171.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-60878.gif)
…………………………10分
(2)由于
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-24953.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054529-31098.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054530-21171.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054536-40157.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054529-45020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054536-49699.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-24953.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054536-25450.gif)
下面先证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-13665.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054536-98033.gif)
Ⅰ)根据
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-24953.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054529-45020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054537-80106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054537-36622.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054537-58912.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054537-95060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054537-40287.gif)
Ⅱ)假设结论对
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054538-95006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054538-96133.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054538-33560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054538-20888.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054539-59305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054539-94985.gif)
即当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054535-33728.gif)
综合Ⅰ),Ⅱ)可知,不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054536-98033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-13665.gif)
于是当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054531-13665.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054539-15483.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054539-67221.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054539-62851.gif)
…………………………20分
核心考点
举一反三
A.15 | B.1![]() | C.17 | D.18 |
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054504-18257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054504-25487.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054505-40534.gif)
A.3 | B.4 | C.6 | D.12 |
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054457-96536.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054457-82394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054458-58138.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054458-29059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054458-81964.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054441-30543.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054441-91382.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054441-36427.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054441-24929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054441-86877.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054442-70509.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054442-23768.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054442-39066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054442-58360.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054443-29272.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054443-27008.gif)
(1) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054443-74197.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054443-96693.gif)
(2) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054443-12047.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054444-62618.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054444-97014.gif)
(3) 证明存在
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054444-81674.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054444-16725.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054444-81674.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013054430-27705.gif)
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