What values of z in the complex plane make the series absolutely convergent?

[heman]

Hi,
In this Problem i am finding Problem to calculate the set of z:
Pls help
Determine all z \subset C for which the following series is absolutely convergent:

\sum (1/n!)(1/z)^n

Thx

 

[Galileo]

Do the terms look familiar? What if you set w=\frac{1}{z}?

 

[heman]

okay ...but generally how to solve such kind of problems..can u be more logical pls

 

[matt grime]

Use the ratio test (and i don't think you should accuse others of not being logical. pointing out that this is the series for exp{1/z} give or take a constant is very logical. you ought to put in the limits too).

 

[heman]

its just my concepts are not clear...how can i accuse anyone here..i have learned a lot from ppl here and i want to improve
Sometimes even in my class i end up asking such stupid questions that whole class bursts into laughter..
Thx for it and urs reply in pm...