题目内容
(本题满分12分) 已知点(1,
)是函数
且
)的图象上一点,等比数列
的前
项和为
,数列![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115830475.png)
的首项为
,且前
项和
满足
-
=
+
(
).
(1)求数列
和
的通项公式;
(2)若数列{
前
项和为
,问
>
的最小正整数
是多少?
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115659325.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115705730.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115721377.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115752457.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115799297.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115815524.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115830475.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115861556.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115877249.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115799297.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115908388.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115908388.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115955426.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115971446.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115986420.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116017435.png)
(1)求数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115752457.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115830475.png)
(2)若数列{
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116205590.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115799297.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116251373.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116251373.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116283537.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194115799297.png)
解:(1)
,
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116423986.png)
,
.
又数列
成等比数列,
,所以
;又公比
,所以
;
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116766557.png)
又
,
,
;
数列
构成一个首相为1公差为1的等差数列,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116829195.png)
当
,
;
(
);
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941170311144.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941170471467.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941170941007.png)
由
得
,满足
的最小正整数为112.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116345772.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116376931.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116392793.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116423986.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116439438.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941164541232.png)
又数列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116485481.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941165011306.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116517304.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116532660.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941166881189.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116704523.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941167191743.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116766557.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116766488.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116782561.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116813651.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116829195.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116844632.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116829195.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116891836.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116907223.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116938537.png)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116017435.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941169691037.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194117000600.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194116704523.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941170311144.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941170471467.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941170632276.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231941170941007.png)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194117203939.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194117219591.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823194117234723.png)
略
![](http://thumb.zyjl.cn/images/loading.gif)
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