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Limit in Complex Field

  1. Mar 6, 2010 #1
    Could someone please provide me a little direction.
    I'm trying to show this sequence converges

    [tex]x_n=n\left(e^{\frac{2\pi i}{n}}-1\right)[/tex]

    I know [tex]\lim_{n\rightarrow\infty}|x_n|=2\pi i[/tex], but I have no idea how to arrive at the solution.

    This is not a homework question.
  2. jcsd
  3. Mar 6, 2010 #2


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    The obvious thing to do would be to expand the exponential term as a power series.
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