高等数学教学案例改革探讨——单调有界数列引例

Discussion on Case Reform of Higher Mathematics Teaching—Examples of Monotone Bounded Sequence

摘要: 单调有界数列存在极限，如果给出的单调有界数列的例子容易理解和接受对大家掌握知识更有帮助。我们给出了单位圆内接正多边形的面积和周长组成的单调递增有上界数列，两个单调递减有下界的数列，并给出了每个数列单调性和有界性的严格证明。

Abstract: The monotone bounded sequence has a limit, and it will be more helpful to master the knowledge if the examples given are easy to understand and accept. In this paper, we give a monotone increasing sequence with upper bound consisting of the area and perimeter of a regular polygon within a unit circle and two monotone decreasing sequences with lower bound, and give a strict proof of monotone and boundedness of each sequence.