there are some mathematical restrictions on this

就会有些数学限制
because there are infinite number of terms in this thing.

因为这个式子有无穷多项
When you add them all up

当你把它们加起来
you may get infinity which would be nonsense.

可能得到无穷大那就没有意义了
So, you should really sum up this infinite number of terms

因此如果它们的和是收敛的
if they add up to a finite number,

你就应该把这无穷多项加起来
and if they do that will give you the function here.

如果确实收敛就能得到这个函数
What we have done is to just use the first two terms as an approximation.

我们所做的就是取前两项做近似计算
Or what I'm telling you is that

我刚才所讲的
there is something called The Taylor Expansion of a function

这个式子叫做函数的泰勒展开式
that allows you to know the function even here, macroscopically,

在已知任意阶导数的情况下
far from here if you knew all the derivatives.

它甚至可以算出一段距离外的函数式