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用递推关系式求数列的通项公式,是高中学生们的一个难点,也是高中阶段的一个重点内容.运用转化的思想,把所求数列的递推关系式转化为我们所熟悉的“等差数列”型或“等比数列”型,然后用相应的方法求出其通项公式.常见的方法有“累加法”(知道差式)和“累乘法”(知道商式)等等.这里我选用一教师教案中的三个例题,向同学们介绍一条新的思考途径——构常数列求通项公式.为对比起见,先写出该教师在那节课对三例所讲解的方法.
Using the recursion relation to find the general term formula of the series is a difficult point for high school students and a key content for the high school stage. Using the idea of transformation, the recurrence relation of the number sequence is transformed into the one we are familiar with. Arithmetic series “type or ” is equal to the number “ type, and then use the corresponding method to find out its general term formula. Common methods are ”accumulation " (keep the difference type) and (Know commerce) etc. Here I use three example questions from a teacher’s lesson plan to introduce a new way of thinking to the students - to construct a constant column formula for the general term. For the sake of comparison, first write the teacher there. Lessons explained in three cases.