名校
解题方法
1 . 已知
为各项均为正数的数列且对满足
的正整数p,q,n都有等式
成立.
(1)判断数列
是否满足等式(*);
(2)证明
的充要条件为
,
;
(3)证明:存在与
有关的常数
,使得对于每个正整数n,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b221847bc9fb81ccd5cba45f544eb70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a505f9f4d33acfa375f4b4fde55ef025.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60cd8687ed35d6fba1c08609619d4305.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c259287666b28c29be312a668dcdce90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c6a0fbf3fef458d93d7b936acc17ef.png)
(3)证明:存在与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d30d43c61b4c81f50d9103df9a46e9.png)
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