题文
设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.![设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D. 设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D.](https://www.mshxw.com/file/tupian/20210919/16c706d1389709e382d99e58faf9d42c.gif)
B.
![设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D. 设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D.](https://www.mshxw.com/file/tupian/20210919/4942b9d7f6ee0df88fd3298e72485d9a.gif)
C.
![设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D. 设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D.](https://www.mshxw.com/file/tupian/20210919/d65b3c6c3e2b3485301ec90b70e5a458.gif)
D.
![设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D. 设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D.](https://www.mshxw.com/file/tupian/20210919/765dec0482b08a2243302c7cd802d440.gif)
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答案
D解析
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考点
据考高分专家说,试题“设数列{(-1)n}的前n项.....”主要考查你对 [等比数列的前n项和 ]考点的理解。 等比数列的前n项和等比数列的前n项和公式:
等比数列中设元技巧:
已知a1,q,n,an ,Sn中的三个量,求其它两个量,是归结为解方程组问题,知三求二。
注意设元的技巧,如奇数个成等比数列,可设为:…![设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D. 设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D.](https://www.mshxw.com/file/tupian/20210919/20120829164021819981.png)
,…(公比为q),但偶数个数成等比数列时,不能设为…![设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D. 设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D.](https://www.mshxw.com/file/tupian/20210919/20120829164021838904.png)
,…因公比不一定为一个正数,公比为正时可如此设。
等比数列前n项和公式的变形:
q≠1时,![设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D. 设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D.](https://www.mshxw.com/file/tupian/20210919/201208291640218571261.png)
(a≠0,b≠0,a+b=0);
等比数列前n项和常见结论:
一个等比数列有3n项,若前n项之和为S1,中间n项之和为S2,最后n项之和为S3,当q≠-1时,S1,S2,S3为等比数列。


![设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D. 设数列{(-1)n}的前n项和为Sn,则对任意正整数n,Sn= [ ]A.B.C.D.](https://www.mshxw.com/file/tupian/20210919/20111223090918001.gif)
