# radius of convergence and interval of convergence of the series

• May 1st 2010, 09:08 PM
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radius of convergence and interval of convergence of the series
$\sum_{n=1}^{\infty} \frac{n}{7^n} (x + 4)^n$

I used the ratio test and after some cancellations, i get

$\sum_{n=1}^{\infty} \frac{n+1}{n} * \frac{x+4}{7}$

not sure if what i got so far is correct but i get stuck after i get to this part.

How do i finish this problem? thanks!
• May 1st 2010, 09:14 PM
jcmc2112
After applying the ratio test, you should get
$\underset{n\rightarrow\infty}{\lim}\frac{n+1}{n}*\ frac{x+4}{7}$
instead of another sigma.

To find the radius of convergence, you simply have to find the values of x that would make the series converge.
• May 1st 2010, 09:22 PM
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ahh silly mistake from me. forgot about that. thanks!