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数列是离散型函数,是特殊的函数,所以对于一些数列问题,学生会尝试用函数的思想来解决,往往会有意想不到的效果。对于数列中的单调性问题,学生经常会想到利用导数求解。但是由于没有深刻认识到数列是离散型函数,在解题过程中经常会犯一些错误。本文旨在引导学生认识到错误产生的原因并学会解决此类问题。
The sequence is a discrete function, a special function, so for some sequence problems, students will try to use the idea of function to solve, often have unexpected results. For monotonic problems in series, students often think of using derivative solutions. However, since there is no profound recognition that the series is a discrete function, some mistakes are often made in solving the problem. This article aims to guide students to recognize the causes of errors and learn to solve such problems.