已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025924310388.png)
是等差數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025924310481.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025924326297.png)
項和,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025924341678.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025924357347.png)
等于( )
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科目:高中數(shù)學
來源:不詳
題型:解答題
已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053691481.png)
為等比數(shù)列,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053706875.png)
是等差數(shù)列,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240310537221038.png)
(Ⅰ)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053738491.png)
的通項公式及前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053753297.png)
項和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053769388.png)
;
(2)設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053784697.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053800494.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053800739.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053816506.png)
,其中
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053831539.png)
,試比較
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053847373.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824031053862391.png)
的大小,并加以證明.
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科目:高中數(shù)學
來源:不詳
題型:解答題
設(shè)數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030502316456.png)
的前n項和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030502331388.png)
,已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030502347466.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030502363850.png)
,數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030502378471.png)
是公差為d的等差數(shù)列,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030502394523.png)
.
(1)求d的值;
(2)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030502316456.png)
的通項公式;
(3)求證:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240305024251525.png)
.
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科目:高中數(shù)學
來源:不詳
題型:解答題
已知等差數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025912017492.png)
的前n項和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025912033376.png)
,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025912048436.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025912064571.png)
.
(Ⅰ)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025912017492.png)
的通項
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025912095361.png)
;
(Ⅱ)設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025912111675.png)
,求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025912142499.png)
的前n項和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025912142368.png)
.
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:解答題
已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708574481.png)
是正數(shù)組成的數(shù)列,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708590371.png)
,且點
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708605943.png)
在函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708621515.png)
的圖象上.
(Ⅰ)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708574481.png)
的通項公式;
(Ⅱ)若數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708652479.png)
滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708668389.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708683671.png)
,求證:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708699169.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025708714624.png)
.
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科目:高中數(shù)學
來源:不詳
題型:解答題
設(shè)等比數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448033481.png)
的首項為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448049415.png)
,公比為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448065311.png)
(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448065311.png)
為正整數(shù)),且滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448096432.png)
是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448127399.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448143346.png)
的等差中項;數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448143491.png)
滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240254481741055.png)
(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448189686.png)
).
(Ⅰ)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448033481.png)
的通項公式;
(Ⅱ)試確定
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448221267.png)
的值,使得數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448143491.png)
為等差數(shù)列;
(Ⅲ)當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448143491.png)
為等差數(shù)列時,對每個正整數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448267313.png)
,在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448299358.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448408399.png)
之間插入
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448423366.png)
個2,得到一個新數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448439450.png)
. 設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448455373.png)
是數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448439450.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448486297.png)
項和,試求滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448501576.png)
的所有正整數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824025448517337.png)
.
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科目:高中數(shù)學
來源:不詳
題型:解答題
數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926033480.png)
前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926080297.png)
項和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926096633.png)
,數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926096487.png)
滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926127646.png)
(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926127695.png)
),
(1)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926033480.png)
的通項公式;
(2)求證:當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926158505.png)
時,數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926174583.png)
為等比數(shù)列;
(3)在題(2)的條件下,設(shè)數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926096487.png)
的前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926080297.png)
項和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926220373.png)
,若數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926236492.png)
中只有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926252361.png)
最小,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824024926267325.png)
的取值范圍.
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科目:高中數(shù)學
來源:不詳
題型:單選題
等差數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030111311451.png)
的前n項和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030111326388.png)
,且滿足
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030111373878.png)
,則下列數(shù)中恒為常數(shù)的是( �。�
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科目:高中數(shù)學
來源:不詳
題型:單選題
設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030153072473.png)
為等差數(shù)列,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030153103803.png)
,則數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030153072473.png)
的前13項的和為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824030153134416.png)
( )
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