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数列是高中数学的重要内容,它与数、式、函数、方程、不等式有着密切的联系,是每年高考的必考内容.同时数列综合问题中蕴含着许多数学思想与方法(如函数、方程思想、分类讨论思想、化归与转化思想等).在处理数列综合问题时,若能灵活运用这些数学思想与方法,则会取得事半功倍的效果.一、函数思想数列是一类特殊的函数——a_n,S_n都是变量为n的函数,因此求函数值、判别单调性、利用图象等方法都适用于数列.
The sequence is an important part of high school mathematics, and it is closely related to numbers, formulas, functions, equations and inequalities, and is the compulsory part of the annual college entrance examination. Meanwhile, there are many mathematical ideas and methods (such as functions and equations , Classification discussion thinking, conversion and conversion thought, etc.) When dealing with the problem of sequence synthesis, if we can flexibly use these mathematical ideas and methods, we will achieve a multiplier effect.First, the sequence of function ideas is a special kind of function - Since a_n and S_n are all variables whose function is n, finding the value of a function, judging monotonicity, and using images are all applicable to the sequence.