And we did that in kind of the intuition behind the binomial theorem videos.

我们是在利用二项式定理的方法来解决问题。

If you, don't a positive integer the binomial theorem, Newton's binomial theorem will give you an infinite sum.

如果你不知道二项式定理中的正整数，牛顿二项式定理将给出一个无穷和。

This week, we will begin to study the binomial theorem.

这周我们要开始学二项式定理。

Putting N equals a half into the binomial theorem he gets an infinite series.

将 N 等于一半代入二项式定理，他得到了一个无穷级数。

The standard binomial theorem insist that you apply it only when N is a positive integer, which makes sense.

标准二项式定理坚持只有当 N 为正整数时才应用它，这是有道理的。

And you might want to watch some of the probability videos on this when I talk about the binomial theorem and all that.

当我谈论二项式定理和所有其他内容时，您可能想观看一些关于此的概率视频。

And you can extend the pattern for all negative integers either using the binomial theorem or just looking at what numbers would add together to make the numbers underneath.

您可以使用二项式定理或仅查看哪些数字可以加在一起形成下面的数字，来扩展所有负整数的模式。

And that's pretty neat because when you just see it in kind of a vacuum-- if you have no context for it, you wouldn't guess that this is in any way related to the binomial theorem.

这非常巧妙，因为当你只是在某种真空中看到它时——如果你没有它的上下文，你不会猜到它与二项式定理有任何关系。

So Newton is convinced the binomial theorem works even for negative values of N, which means there's more to Pascal's triangle above the zeroeth you could add a zero and a one that add to make that first one.

因此，牛顿确信二项式定理即使适用于 N 的负值，这意味着帕斯卡三角形中除了零之外还有更多内容，您可以添加一个零和一个一，将它们相加得到第一个。