题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211542-21165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211543-75719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211543-29757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211548-33856.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211549-16003.png)
解析
试题分析:由于
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211549-81087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211549-96119.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211549-26099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211550-91122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211550-18467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211550-11896.png)
上述四个等式累加得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211550-22318.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211550-57387.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211521-77002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211522-71765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211522-65956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211522-39926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211522-39378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211523-35430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211523-89849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211523-33493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211523-68592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211523-88972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-92850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-25108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-78508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-11092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211525-95294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211525-95294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-25108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-78508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-78508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211525-95294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211525-95294.png)
(1)若各项均为正整数的数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-92850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-11092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-78508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211525-30428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211525-95294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211525-95294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-92850.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211523-88972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-92850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211525-98448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211525-57732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211526-34510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211524-11092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211523-33493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211521-77002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211526-24547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211522-39926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211445-48035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211445-98371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211445-64190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211445-50194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211446-48982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211446-63531.png)
(1)求数列{an}的通项公式;
(2)求数列{|an|}的前n项和.
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211425-96771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211425-49764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211425-70213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211425-62400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211404-40524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211404-71518.png)
等级 | 等级图标 | 需要天数 | 等级 | 等级图标 | 需要天数 |
1 | ![]() | 5 | 7 | ![]() ![]() ![]() ![]() | 77 |
2 | ![]() ![]() | 12 | 8 | ![]() ![]() | 96 |
3 | ![]() ![]() ![]() | 21 | 12 | ![]() ![]() ![]() | 192 |
4 | ![]() | 32 | 16 | ![]() | 320 |
5 | ![]() ![]() | 45 | 32 | ![]() ![]() | 1152 |
6 | ![]() ![]() ![]() | 60 | 48 | ![]() ![]() ![]() | 2496 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211405-41045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211405-15314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211342-46334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211343-59944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211343-84606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211343-61662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211343-84108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211350-37460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211350-99657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211350-31093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211350-98573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211351-75339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211351-10442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211351-42562.png)
(1)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211352-55929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211352-22608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211352-97594.png)
(2)试证明对于数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211352-35192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211353-76950.png)
(3)若等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211342-46334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211353-60389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211353-97120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211353-76950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011211353-76950.png)
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