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数形结合方法沟通了“数”与“形”之间的联系,“数”因“形”而直观,“形”因“数”而深刻.数形结合已成为解题的重要方法,但在运用数形结合方法时,有时容易犯经验主义错误,以偏概全.一、错误迁移例1通项公式为an=an2+n的数列{an},若满足a1an+1对n≥8恒成立,求实数a的取值范围.解当n≥8时,an>an+1恒成立,即a11<-,只要1a<--.2n+1(2n+1)=min17
The combination of number and form communicates the connection between “number” and “shape” and “number” is intuitive because of “shape” and “shape” because of “number”. Number combination has become an important method of solving problems, but in the use of digital combination method, it is easy to commit empiricist mistakes, in order to be generalized. First, the wrong transfer Example 1 The general formula for the sequence an = an2 + n { an}, an> an + 1 holds if a1 an + 1 holds true for n≥8. , That is, a11 <-, as long as 1a <-. 2n + 1 (2n + 1) = min17