# Math Help - Finding sumfunctions for power series

1. ## Finding sumfunctions for power series

Hello

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

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

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

Or am i totally off here?

2. $|x+7|<1,$ now check the endpoints.

3. Originally Posted by Krizalid
$|x+7|<1,$ now check the endpoints.
Yes thats what i came up with too, but i tried to calc it in maple using:

Sum((2*n+1)*((x+7)^n), n=0..infinity); simplify(value(%));

Which gave me $\frac{x+8}{(x+6)^2}$