名校
解题方法
1 . 如果数列
满足“对任意正整数i,j,
,都存在正整数k,使得
”,则称数列
具有“性质P”.已知数列是无穷项的等差数列,公差为d.
(1)若
,
,判断数列
是否具有“性质P”,并说明理由;
(2)若数列
具有“性质P”,求证:
且
;
(3)若数列
具有“性质P”,且存在正整数k,使得
,这样的数列共有多少个?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab406d94b4907ab8a20ae3214628b045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3b18d23d41e5f456dfd6485feed523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3068733ef2ceda9f1620d5c9bcdfa542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8e68eb4ade6e22982d2df5102d8894.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0af74258551ca3f28b2c6ce54bffd1.png)
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