The discussion centers on the convergence of a power series centered at 0, specifically addressing a homework question regarding its interval of convergence. Participants clarify that if the series converges at a point x=a, it converges for |x|<|a|, and if it diverges at x=a, it diverges for |x|>|a|. The correct answer to the homework question is confirmed to be D, with emphasis on the importance of considering absolute values in the analysis of convergence.
PREREQUISITESStudents studying calculus, particularly those focusing on series and convergence, as well as educators looking to clarify concepts related to power series.
izelkay said:Homework Statement
Can anyone explain to me why the answer to this question is D?:
http://puu.sh/2FoET.png
The Attempt at a Solution
I'm not really sure where to begin, except I know that the series is centered at 0. I was also thinking that the given x's was the Interval of Convergence, but then, that wouldn't really make sense with the series centered at 0.
Dick said:What do you know about convergence of a power series centered at 0? I know that if it converges at x=a then it converges for |x|<|a|. I also know that if it diverges at x=a then it diverges for |x|>|a|.