$($a$)(3$ points$)$ For what value of $c$ does the sequence $((\frac{nc}{n-c}{)}^n{)}_n=1^{}$ converge to $16?$

$($b$)(5$ points$)$ For what value$($s$)$ of $c$ does the series below converge?

${\displaystyle \underset{n=0}{\overset{}{}}}({\displaystyle \underset{c}{\overset{}{}}}\frac{2}{1x^2}dx{)}^n$