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Complex Analysis: Radius of Convergence

  • Thread starter gbean
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  • #1
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Homework Statement


Find the radius of convergence of the power series:
a) [tex]\sum[/tex] z[tex]^{n!}[/tex]
n=0 to infinity

b) [tex]\sum[/tex] (n+2[tex]^{n}[/tex])z[tex]^{n}[/tex]
n=0 to infinity

Homework Equations


Radius = 1/(limsup n=>infinity |cn|^1/n)


The Attempt at a Solution


a) Is cn in this case just 1? And plugging it in, the radius is 1?

b) cn = n+2[tex]^{n}[/tex], so then limsup n=> infinity |n+2[tex]^{n}[/tex]|[tex]^{1/n}[/tex] => ?? I'm stuck at this point.

i'm also confused in general, is cn just a sequence of coefficients, and what is zn? And I have other formulas for figuring out the radius of convergence, such as the ratio test. I'm not sure when to use which methods. Thank you!
 

Answers and Replies

  • #2
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I also don't understand why z^n isn't used in the calculation of the radius of convergence.
 
  • #3
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So I'm running into trouble for part b still, any help would be greatly appreciated. The answer key says 1/2, but I don't know how to derive that.
 

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