Calculate the sum of the next series and for which values of $x$ it converges:
I used D'Alembert and found that the limit is less than 1, so: $-5 < x < 1$ (because the fraction must be less than 1).
and then I assigned the values: $x=-5$ and $x=1$ in the series and got:
for $x=-5$ and $x=1$, it diverges.
then the series converges in the range of $(-5,1)$, $R=3$ and the center point is for $x=2$.
Please let know if there is a mistake and find the sum.