\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For the function \(f(x)=\frac{1}{1-x}\),
  1. Find \(f^{(1)}(x)\), \(f^{(2)}(x)\), and \(f^{(3)}(x)\).
  2. Find \(f(0)\), \(f'(0)\), \(f^{(2)}(0)\), and \(f^{(3)}(0)\).
  3. Show that the Maclaurin series for \(\frac{1}{1-x}\) is$$ \frac{1}{1-x} = 1 + x + x^2 + x^3 + \dots = \sum_{k=0}^\infty x^k $$

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