“微积分二：数列与级数”将介绍数列、无穷级数、收敛判别法和泰勒级数。本课程不仅仅满足于得到答案，而且要做到知其然，并知其所以然。

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From the course by The Ohio State University

微积分二: 数列与级数 (中文版)

45 ratings

The Ohio State University

45 ratings

“微积分二：数列与级数”将介绍数列、无穷级数、收敛判别法和泰勒级数。本课程不仅仅满足于得到答案，而且要做到知其然，并知其所以然。

From the lesson

数列

欢迎参加本课程！我是 Jim Fowler，非常高兴大家来参加我的课程。在这第一个模块中，我们将介绍第一个学习课题：数列。简单来说，数列是一串无穷尽的数字；由于数列是“永无止尽”的，因此仅列出几个项是远远不够的，我们通常给出一个规则或一个递归公式。关于数列，有许多有趣的问题。一个问题是我们的数列是否会特别接近某个数；这是数列极限背后的概念。

- Jim Fowler, PhDProfessor

Mathematics

Finding limits is hard. I wish I could just prove that they exist. [SOUND] Here's a theorem that guarantees a sequence converges. If the sequence is bounded and monotone, then the limit exists. Why is this important? Well, I often can't tell whether a sequence converges. But I may be able to show that a sequence is both bounded and monotone. And then I know it has a limit. But why should I believe that the Monotone Convergence Theorem is true? Well, let's think about this geometrically. Suppose I've got a number line and I've got terms of my sequence, x sub 1, x sub 2, x sub 3. Let's pretend they are increasing, and let's pretend that the sequence is bounded. So, I know that the sequence never exceeds this value B.

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