\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
  1. Starting with the geometric series \(\frac{1}{1-u} = 1+u+u^2+\dots\), use a substitution to find the Maclaurin series for \(\frac{1}{1+t^2}\).
  2. By integrating the resulting series from \(0\) to \(x\), find the Maclaurin series for \(f(x) = \arctan(x)\).

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