Complex Analysis: Radius of Convergence

  • Thread starter gbean
  • Start date
  • #1
gbean
43
0

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
gbean
43
0
I also don't understand why z^n isn't used in the calculation of the radius of convergence.
 
  • #3
gbean
43
0
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.
 

Suggested for: Complex Analysis: Radius of Convergence

  • Last Post
Replies
4
Views
485
  • Last Post
Replies
23
Views
595
Replies
4
Views
143
  • Last Post
Replies
1
Views
258
  • Last Post
Replies
3
Views
984
Replies
7
Views
390
Replies
4
Views
424
  • Last Post
Replies
8
Views
574
  • Last Post
Replies
10
Views
179
Replies
7
Views
461
Top