Homework$-9$: Problem $7$

$(8$ points$)$

Find the interval of convergence for the given power series.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n^{10}(x+8{)}^n}{(7^n)(n^{\frac{32}{3}})}$

The series is convergent:

from $x=q,$ left end included $(Y,N)$: $q,$

to $x=q,$ right end included $($Y$,$N$)$: