anonymous
  • anonymous
find the radius of the convergence of the Taylor series around x=0 for ln(1-x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
i guess it cannot be bigger than one, since log (0) i undefined.
anonymous
  • anonymous
we can compute it if you like
anonymous
  • anonymous
standard trick is to take the derivative get \[-\frac{1}{1-x}\], write the expansion for that one and then integrate term by term

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anonymous
  • anonymous
get \[-\sum\frac{x^k}{k}\]
anonymous
  • anonymous
ratio test immediately tells you radius of convergence is 1

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