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Ask yourself what that does as n goes to infinity in case |z|<1, =1, >1. You might recall that <math>nr^n\to 0</math> as <math>n\to\infty</math> if <math>|r|<1</math>. --[[User:Bell|Steve Bell]] | Ask yourself what that does as n goes to infinity in case |z|<1, =1, >1. You might recall that <math>nr^n\to 0</math> as <math>n\to\infty</math> if <math>|r|<1</math>. --[[User:Bell|Steve Bell]] | ||
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| + | On Problem 1 from the practice problems I was thinking Liouville's theorem, but that is for a bounded entire function. I seem to vaguely recall this being shown with an analytic function which is bounded over a closed region, but I can't seem to find it in my notes. Anyone have this?--[[User:Rgilhamw|Rgilhamw]] 16:35, 14 November 2009 (UTC) | ||
Revision as of 12:35, 14 November 2009
Discussion area to prepare for Exam 2
To find the radius of convergence of $ \sum_{n=0}^\infty (n!)z^{n!} $, you'll need to use the Ratio Test.
$ \frac{u_{n+1}}{u_n}=\frac{(n+1)!z^{(n+1)!}}{n!z^{n!}}=(n+1)z^{n\cdot n!} $.
Ask yourself what that does as n goes to infinity in case |z|<1, =1, >1. You might recall that $ nr^n\to 0 $ as $ n\to\infty $ if $ |r|<1 $. --Steve Bell
On Problem 1 from the practice problems I was thinking Liouville's theorem, but that is for a bounded entire function. I seem to vaguely recall this being shown with an analytic function which is bounded over a closed region, but I can't seem to find it in my notes. Anyone have this?--Rgilhamw 16:35, 14 November 2009 (UTC)
