已知等差數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044328283481.png)
的公差
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044328299443.png)
,若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044328299524.png)
成等比數(shù)列,那么公比為( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知公比不為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858333206.png)
的等比數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858349456.png)
的首項
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858364481.png)
,前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858380297.png)
項和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858395388.png)
,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858411724.png)
成等差數(shù)列.
(1)求等比數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858349456.png)
的通項公式;
(2)對
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858442498.png)
,在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858458348.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858473400.png)
之間插入
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858489353.png)
個數(shù),使這
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858505461.png)
個數(shù)成等差數(shù)列,記插入的這
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858489353.png)
個數(shù)的和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858536365.png)
,求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858551471.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858380297.png)
項和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044858583373.png)
.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438827545.png)
是首項為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438842335.png)
,公差為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438858347.png)
的等差數(shù)列(d≠0),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438873373.png)
是其前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438889327.png)
項和.記b
n=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438905609.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438920421.png)
,其中
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438951270.png)
為實數(shù).
(1) 若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438967375.png)
,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438967357.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438998365.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044439014366.png)
成等比數(shù)列,證明:S
nk=n
2S
k(k,n∈N
+);
(2) 若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044439029439.png)
是等差數(shù)列,證明:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044438967375.png)
.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340093481.png)
是首項為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340108559.png)
,公差為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340124291.png)
的等差數(shù)列,其前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340139297.png)
項和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340155388.png)
,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340171653.png)
成等差數(shù)列.
(1)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340093481.png)
的通項公式;
(2)記
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340186609.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340139297.png)
項和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340233373.png)
,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044340233373.png)
.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044154215457.png)
滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240441542311455.png)
(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044154262237.png)
為常數(shù),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044154278520.png)
)
(1)當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044154293364.png)
時,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044154309348.png)
;
(2)當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044154340305.png)
時,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044154356450.png)
的值;
(3)問:使
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044154371492.png)
恒成立的常數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044154262237.png)
是否存在?并證明你的結(jié)論.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044101113477.png)
滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044101113635.png)
,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044101128409.png)
,設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044101113477.png)
的
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044101159277.png)
項和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044101175388.png)
,則使得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044101175388.png)
取得最大值的序號
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044101159277.png)
的值為( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
在數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824043848559794.png)
中,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824043848575262.png)
等于( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
若數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044349531456.png)
滿足:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240443495461239.png)
,則該數(shù)列的通項公式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044349577348.png)
=__________。
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
設(shè)等差數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824043322051480.png)
中首項為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824043322066455.png)
公差為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824043322082320.png)
,且從第5項開始是正數(shù),則公差
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824043322082320.png)
的范圍是( ).
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