18-19高一下·上海浦东新·期末
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1 . (1)证明:
;
(2)证明:对任何正整数n,存在多项式函数
,使得
对所有实数x均成立,其中
均为整数,当n为奇数时,
,当n为偶数时,
;
(3)利用(2)的结论判断
是否为有理数?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d969abdb2f6638663e80e15bffd247.png)
(2)证明:对任何正整数n,存在多项式函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2b21d31f1bb8801b0117b49086a634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68a728745bb3bd33917dc715c4fc945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd42f8e3f220a7b1c6f6945e73bc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feaffe7219b4b165cf67c7751dff8876.png)
(3)利用(2)的结论判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d82121ba82f39bb5e8068bd11ed6d74.png)
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