I need to find the sumfunction and the radius of convergence + convergence range for the following:

\(\displaystyle \sum_{n=0}^{\infty} (2n+1)(x+7)^n\)

What i did was this:

\(\displaystyle \lim_{n\rightarrow\infty} \frac{2n+1}{2(n+1)+1}=\lim_{n\rightarrow\infty} \frac{2n+1}{2(n+3)}\) which converges to 1 for \(\displaystyle n\rightarrow\infty\) so radius of convergense is 1, but what is the convergence range?

Or am i totally off here?