Consider the infinite series ${\displaystyle \underset{k=1}{\overset{}{}}}\frac{8k^2}{5^k}.$

Apply the Ratio Test.

$\underset{k}{lim}|\frac{a_{k+1}}{a_k}|=$

$,$ which is

So we can conclude that the series ${\displaystyle \underset{k=1}{\overset{}{}}}\frac{8k^2}{5^k}$