1 . 已知正实数列
满足
,当
时,记集合
,且集合
中的最大元素为
.
(1)若
,求数列
的通项公式;
(2)记数列前n项和为
,证明:存在正实数
,对于任意的正实数
与整数n>1,都有
.注:对于任意实数a,b,定义
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10b321b66145a2ed6b30d30b62fd8acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7afe76f3b456f040fef0d89e0f2996f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191a66915ee31c2c7e0a0ace99df4586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列前n项和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bc85af36f64be115dd7c5d88fac6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c0e8564359b3f5bd268ab136314f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478e75f2162f25b93d4c337e2829fc05.png)
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2 . 已知数列
,
,
是
的前
项和,且
.
(Ⅰ)求
,
;
(Ⅱ)猜想
的表达式,并用数学归纳法证明;
(Ⅲ)以
为坐标的点
是否都落在同一直线上?若是,求出该直线方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](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/4d0a77b7f47968db860b049b9726a309.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(Ⅱ)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(Ⅲ)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fd43745357381c3b577a87883ae156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6136317c8df5fc1cf4afbf4ff8274d5.png)
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