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Ted123
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Homework Statement
[PLAIN]http://img225.imageshack.us/img225/7501/complexh.jpg
Homework Equations
The Attempt at a Solution
Can I say that, for both [itex]|z|<1[/itex] and [itex]|z|>1[/itex] ,
[itex]\displaystyle \left | \frac{1}{n^2} \left ( \frac{1}{1+z^n} \right ) \right | \leq \frac{1}{n^2}[/itex] .
So, since [itex]\displaystyle \sum^{\infty}_{n=1} \frac{1}{n^2}[/itex] converges, [itex]\displaystyle \sum^{\infty}_{n=1} \frac{1}{n^2} \left ( \frac{1}{1+z^n} \right )[/itex] converges absolutely in both cases (a) and (b) by the comparison test?
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