Convergence of x_n: Limit in Complex Field

BSCowboy · Mar 6, 2010

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.

nicksauce · Mar 6, 2010

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

Convergence of x_n: Limit in Complex Field

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Convergence of x_n: Limit in Complex Field

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