Can you make sure I'm doing this right?

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SUMMARY

The discussion centers on the convergence of the series ∑z-n and its correct formulation based on the value of |z|. For |z|>1, the series converges to 1/(z-1), while for |z|<1, it converges to 1/(1-z). A participant questions the validity of the equation for |z|>1, suggesting that it should be expressed as ∑(1/z^n) = z/(z-1). This indicates a need for clarity in the application of convergence formulas in complex analysis.

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Homework Statement



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Homework Equations



If |z|>1, the series ∑z-n converges to 1/(z-1)

If |z|<1, the series ∑zn converges to 1/(1-z)

The Attempt at a Solution



screen-capture-7-3.png




? Am I getting there?
 
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Jamin2112 said:

Homework Equations



If |z|>1, the series ∑z-n converges to 1/(z-1)

I don't think that equation is right... Shouldn't it be for |z|>1,
[tex]\sum_{n=0}^\infty \frac{1}{z^n} = \frac{1}{1-\frac{1}{z}} = \frac{z}{z-1} \; \; ?[/tex]

Or am I missing something?
 

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