题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113829-90494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113829-11326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113830-63180.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113829-90494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113830-61509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113829-11326.png)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113830-96736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113830-90088.png)
(3)证明:不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-24214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-32757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-35879.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-47330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-18439.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113832-66613.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113830-63180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113832-92156.png)
两式作差
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113832-54368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113832-52495.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113833-36034.png)
第二问中,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113833-23372.png)
第三问中,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113833-93637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113833-51945.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113834-85726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113834-24290.png)
结合放缩法得到。
解:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113830-63180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113832-92156.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113832-54368.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113834-11768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113832-52495.png)
又∵正项数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113829-90494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113834-19725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113833-36034.png)
又n=1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113835-82765.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113835-47256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113829-90494.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-47330.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-18439.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113835-46365.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113835-20375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113835-98803.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113836-72934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113836-96256.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113836-12669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113837-63429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-32757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-35879.png)
∴不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-24214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-32757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113831-35879.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113822-44661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113822-86852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113822-49307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113822-22952.png)
A.6 | B.8 | C.10 | D.11 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113806-59110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113807-70144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113807-56702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113807-51643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113807-98005.png)
A.![]() | B.![]() | C.![]() | D.1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113802-52320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113802-36233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113802-14868.png)
A.21 | B.26 | C.52 | D.70 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113745-68394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113745-30620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113746-20648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113746-74849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113746-22638.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113729-55355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113729-29970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113730-56076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113730-43407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113730-48567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113730-71556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012113731-51536.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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