题目
题型:不详难度:来源:
已知二项式
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175130-47986.png)
(1)若展开式中第五项的二项式系数是第三项系数的
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175130-47094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175130-39841.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175130-39841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-43785.png)
(3)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-48262.png)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-10856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175130-39841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-44896.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-77617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-10856.png)
第二问中,若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175130-39841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-44896.png)
第三问中,因为利用
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175132-48109.png)
解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-77617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-10856.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175130-39841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175131-44896.png)
(3) 法一: (8分)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175132-10869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175132-17632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175132-16880.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175132-19047.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175133-67878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175133-77976.png)
法二:利用
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175132-48109.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175125-59250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175125-53554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175125-52308.png)
A.![]() | B.![]() | C.![]() ![]() | D.![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175118-49118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175118-97408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175113-16913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175113-45598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175104-57060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175104-32754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175105-61248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175105-33069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175105-76909.png)
(2)对于使
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175105-76909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175105-66999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175105-43106.png)
22=1+3 32=1+3+5 42=1+3+5+7
23=3+5 33=7+9+11 43=13+15+17+19
根据上述分解规律,若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175058-54493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175058-79268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020175059-64728.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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