$[-/5$ Points$]$

Consider the following series.

${\displaystyle \underset{n=0}{\overset{}{}}}\frac{(x-7{)}^{n1}}{(n1)9^{n1}}$

Evaluate the following limit where $a_n=\frac{(x-7{)}^{n1}}{(n1)9^{n1}}$

$\underset{n}{lim}|\frac{a_{n1}}{a_n}|$

Find the radius of convergence, $R,$ of the series.

$R=$

Find the interval of convergence of the power series. $($Be sure to include a check for conver finite set of values, enter your answers as a comma$-$separoted list of values.$)$

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