# Math Help - radius of convergence and interval of convergence of the series

1. ## 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!

2. 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.

3. ahh silly mistake from me. forgot about that. thanks!