“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。 注意：此课程的注册将在2018年3月30日结束。如果您在该日期之前注册，您将可以在2018年9月之前访问该课程。

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微积分二: 数列与级数 (中文版)

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“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。 注意：此课程的注册将在2018年3月30日结束。如果您在该日期之前注册，您将可以在2018年9月之前访问该课程。

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

We should introduce a bit of terminology.

[MUSIC]

What's an arithmetic progression?

An arithmetic progression is a sequence with a common difference between

the terms.

We should see an example.

Sequence might begin 5, 12, 19, 26, 33, and

then keep on going.

The general form for the nth term would be 5+7n.

Why is that an arithmetic progression?

Well, the difference between each term to the next is seven, right?

5 plus 7 is 12, 12 plus 7 is 19, 19 plus 7 is 26, 26 plus 7 is 33, and so on.

We can write down a general formula for arithmetic progression.

Well, here we go.

In general, an arithmetic progression will

have the form a sub n = some starting number,

a sub 0 + a common difference times n.

Well, here's another question.

Why are these things even called arithmetic progressions?

Each term is

the arithmetic mean of it's

neighbors.

For reals. Let's look back at that example.

Yeah, in our example, 12 is the arithmetic mean, or the average, of 5 and 19.

because 5 plus 19 is 24.

And 24 divided by 2 is 12.

The same goes for 19.

19 is the arithmetic mean, or the average, of its neighbors.

I'm going to write that down, all right?

19 is the average of 12 and 26.

What's 12 + 26?

It's 38. And 38 divided by 2 is indeed 19.

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