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解题方法
1 . 正项数列:
,满足:
是公差为
的等差数列,
是公比为2的等比数列.
(1)若
,求数列
的所有项的和
;
(2)若
,求
的最大值;
(3)是否存在正整数
,满足
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d745647a5cdac93283f562caa4db9ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d3294e493ff67a13cf897ce29b504b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95f1ac6ae6c0b67c9759c41f7791117.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ac29f1547ada7691187aa1319e3c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1752474698cd5466dd180df0a00ba9c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44b64e92e73f7a74cf43e6f2907d435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce35823c54c666c9ad87537f443cbd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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