I'm not really having problems following the directions and arriving at the correct values, but I'm not really sure what those values mean or what I'm really figuring out.(adsbygoogle = window.adsbygoogle || []).push({});

R = radius of convergence

c = center of the series

Take this one for example.

[tex]\sum\frac{(2x)^{2n}}{(2n)!}[/tex]

Subjecting this to the ratio test gives me:

[tex]\lim_{n\rightarrow \infty}\frac{(2x)^2}{(2n+1)(2n+2)} = 0[/tex]

I get that it doesn't matter what we use for x, we will always get 0. Does that mean that R= all real numbers and is the domain of x?

I think I understand what it means when we get a finite value for R. Does it mean the series will converge if x is any value between -R and +R with c+R and c-R as the endpoints. But what does it mean when we plug in the endpoints values into the original power series and then test for convergence or divergence. Also, why is it useful for us to know this? How does this eventually get applied?

Thanks for any help.

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# Homework Help: Power series

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