Re: Region of convergence

The World Wide Wade wrote:
In article <1189701975.244141@athprx03>,
"I.N. Galidakis" <morpheus@xxxxxxxxxxxx> wrote:

The World Wide Wade wrote:
[snip]

Reread your response and see if it makes any sense to you.

I have no idea what you are talking about. I summarized my response
in a reply to quasi. Please comment there.

It's really quite simple. You responded to my post. Your response was
a lot of nonsense. That's why I asked you to reread it.

I reread it, but I can't find anything wrong with it.

What exactly was "nonsense"? Here's what I wrote:

Hmmm. Even when the root test fails? Suppose sum(a_n*z^n,n=1..oo) is a
convergent complex power series such that:

C = lim sup |a_n|^(1/n) = 1 (1)

Then the root test doesn't tell you anything about convergence, but we know
the
series is convergent anyway.

By (1) the radius of convergence is R = 1/C = 1 regardless, hence the region
of
convergence is a disk.

Unless I made a mistake somewhere.

Do you mind pointing out the "nonsense"?
--
I.N. Galidakis

.

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