题目
题型:不详难度:来源:
分,第(3)小题满分7分.
将边长分别为1、2、3、…、n、n+1、…(
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224556-92763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224556-11662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224556-23518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224556-38854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224557-53473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224557-27289.jpg)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224556-11662.png)
(2)写出
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224557-55433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224556-23518.png)
(3)记
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224557-27998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224557-48635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224558-69898.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224604-34102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224604-16906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224604-54639.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224604-49854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224604-27863.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224556-38854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224605-75733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224605-70313.png)
当n为偶数时,
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224605-57887.png)
当n为大于1的奇数时,
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224605-98485.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224606-98910.png)
(3)由(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224606-57271.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224557-48635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224606-58599.png)
(ⅰ)当n=1时,即
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224606-72888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224606-33611.png)
(ⅱ)当n为偶数时,
即
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224607-71102.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224607-99115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224607-11555.png)
(ⅲ)当n为大于1的奇数时,
即
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224607-21479.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224608-55818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224608-95046.png)
综上所述:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224608-13908.png)
解析
核心考点
试题【(本题满分16分)本题共有3个小题,第(1)小题满分4分,第(2)小题满分5分,第(3)小题满分7分.将边长分别为1、2、3、…、n、n+1、…()的正方形叠放】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224545-68719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224546-98900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224546-18567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224546-10976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224546-74350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224546-82458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224546-98900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224447-38987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224448-18356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224448-51146.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224334-49804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224334-26170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224334-99258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224335-25627.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224334-49804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224334-26170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224334-99258.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224335-70624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224335-17455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224335-17776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224336-70332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224336-98463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224315-44093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224316-26103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224316-30814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224316-84758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224316-77808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224317-48676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224317-74389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224317-67858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224317-55908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224318-42099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224318-45192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224318-69711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224317-48676.png)
记
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224318-97528.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224318-97113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224319-23813.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224319-32769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224317-48676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224319-42798.png)
(3)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224319-10000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224320-79899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224320-81787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224320-51159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224320-98611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224321-41922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224319-23813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224227-65821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224227-84201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224228-34158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224228-58225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224228-53319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224228-73013.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224227-65821.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224229-40619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224229-13419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224229-66669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224228-34158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224229-89973.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224230-35752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224240-18814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010224241-45146.png)
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