# Power Series Question

## Homework Statement

Can anyone explain to me why the answer to this question is D?:

http://puu.sh/2FoET.png [Broken]

## 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.

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Dick
Homework Helper

## Homework Statement

Can anyone explain to me why the answer to this question is D?:

http://puu.sh/2FoET.png [Broken]

## 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.

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|.

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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|.

Oh, I see now. I forgot about the absolute value. Thank you.