来自《耶鲁大学开放课程：基础物理 第16集 第16集》

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  and the whole sum may converge to give a finite answer.
  而这个和可以收敛到一个有限值
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  In which case, it's as good as the function.
  这种情况下它跟原来的函数相等
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  One guy can use 1/(1-x);
  一个人可以用 1/(1-x)
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  the other one can use the infinite series.
  另一个人可以使用无穷级数
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  and they're morally and mathematically in every sense equal,
  并且它们在精神上和数学上一切相等
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  as long as they don't stray outside the region
  只要它们不超出
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  of validity of the infinite series.
  无穷级数的有效范围
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  Ok, so the most popular example
  我在这门课上
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  that I've been using in the class, remember, is (1+x)^n.
  最常用的例子 请记住 是 (1+x)^n
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  That's a function we can do with Taylor series.
  这是一个可以用泰勒级数展开的函数
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  What's the derivative of the function?
  这个函数的导数是什么呢
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  It's n·(1+x)^(n-1), right?
  它是 n·(1+x)^(n-1) 是吧