解题方法
1 . 在等差数列
中,已知
,
.
(1)求通项
及前
项和
;
(2)求
的最大值以及取得最大值时的序号
的值;
(3)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4459ae027bca5885da7d3f34c9c46af7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92701703402f3469541273e511852ba.png)
(1)求通项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91adba8efbf964e9e35547b0fd0ea36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
2 . 已知等差数列
的前
项和为
,且
.
(1)求数列
的通项公式
;
(2)设
,若对一切正整数
,不等式
恒成立,求实数
的取值范围;.
(3)是否存在正整数
,使得
.成等比数列?若存在,求出所有的
;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fce7b028915a4ce6aabf3e7c4e44ffd.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dccd2dd0616ce63e3bb4d9dfe29925dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659ac35d7184a67920f0b0031eaaa3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ad049edd5369dcfb7c2d57a5671472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a9a1061e7fdf435111ef3cf392f0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
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