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集合的概念与表示

> 设数列{a n}满足a 1=a，a n+1=a n 2+a 1，M={a∈R|n∈N*，|a n|≤2}．（1）当a∈（-∞，-2）时，求证：a∉M；（2）当a∈（0， 1 4 ]时，求证：a∈M；（3）当a∈（ 1 4 ，+∞）时，判断元素a与集合M的关系，并证明你的结论．

问题：

发布时间：2024-09-13

设数列{a _n}满足a ₁=a，a _n+1=a _n ²+a ₁，M={a∈R|n∈N*，|a _n|≤2}．
（1）当a∈（-∞，-2）时，求证：a∉M；
（2）当a∈（0，

1

4

]时，求证：a∈M；
（3）当a∈（

1

4

，+∞）时，判断元素a与集合M的关系，并证明你的结论．

参考答案：

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设数列{a n}满足a 1=a，a n+1=a n 2+a 1，M={a∈R|n∈N*，|a n|≤2}． （1）当a∈（-∞，-2）时，求证：a∉M； （2）当a∈（0， 1 4 ]时，求证：a∈M； （3）当a∈（ 1 4 ，+∞）时，判断元素a与集合M的关系，并证明你的结论．

可能感兴趣的题目：

设数列{a _n}满足a ₁=a，a _n+1=a _n ²+a ₁，M={a∈R|n∈N*，|a _n|≤2}．
（1）当a∈（-∞，-2）时，求证：a∉M；
（2）当a∈（0，

1

4

]时，求证：a∈M；
（3）当a∈（

1

4

，+∞）时，判断元素a与集合M的关系，并证明你的结论．