1 . 已知等比数列
的公比为
是
的前
项和.
(1)若
,求
;
(2)若
有无最值?说明理由;
(3)设
,若首项
和
都是正整数,
满足不等式
,且对于任意正整数
有
成立,问:这样的数列
有几个?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab51b5f7f1bfdcbc078245de934414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3569927ec618ca54810d25fb00711b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf9264f3cb48b142d0a58e8eb51463d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ad82582b7d8733b7d323b78a99605f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512d062f56d3d94b4e77c157642a83d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9533056643f05cc760d4a8d71d0811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2 . 已知有穷数列
的各项均不相等,将
的项从大到小重新排序后相应的项数构成新数列
,称
为
的“序数列”.例如:数列
满足
,则其“序数列”
为1,3,2.
(1)若数列
的通项公式为
,写出
的“序数列”;
(2)若项数不少于5项的有穷数列
,
的通项公式分别为
,
,且
的“序数列”与
的“序数列”相同,求实数t的取值范围;
(3)若有穷数列
满足
,
,且
的“序数列”单调递减,
的“序数列”单调递增,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c75058db8f3bce88c1ffd4eadf5f40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0375287e6641a5fa35966d8a0e379f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若项数不少于5项的有穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9d0beddb0070046c8e9e6ab7df805e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0451fd59fddc557f02c7f04c7a84636d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若有穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea6578afabc23f5d7041b88c3790dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdedf06dbbcc2b37f07c9391d8ee2fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ae4e2547c5df93708a8a4e11ee399c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a1ed0b906a67310749d19e98662a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
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