来自《耶鲁大学开放课程：基础物理 第16集 第16集》

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  going from the 0 derivative all the way up to infinity.
  直到无穷阶导数的和
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  And if you do the summation of every value of x, you will get a value,
  对每一个 x 值求和 你都能得到一个值
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  and if that summation is meaningful and gives you a finite number,
  所有项的和是一个有意义的有限值
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  that, in fact, is exactly the function you were given.
  实际上它就是已知的那个函数
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  That is the Taylor series.
  这才是泰勒级数
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  The Taylor series is a series of infinite number of terms which,
  泰勒级数是一系列无穷项
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  if you sum up-- and sum up to something sensible--
  加起来得到有意义的东西
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  will actually be as good as the left-hand side.
  它恰好和左边的相等
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  So, let me give you one example.
  让我来举个例子
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  Here's a famous example.
  这是一个很有名的例子
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  1/(1-x) is the real function.
  1/(1-x) 是实际的函数
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  You and I know this function,
  我们都知道这个函数