Homework$-9$: Problem $10$

$(8$ points$)$

Match each of the power series with its interval of convergence.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(x-6{)}^n}{6^n}$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n!(10x-6{)}^n}{6^n}$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(10x{)}^n}{n^6}$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(x-6{)}^n}{(n!)(6{)}^n}$

A$.(-,)$

B$.\{\frac{6}{10}\}$

C$.\frac{-1}{10},\frac{1}{10}$

D$.(0,12)$