Answer
Diverges
Work Step by Step
Consider $a_n=\dfrac{5^n}{\sqrt n4^n}$ and $b_n=\dfrac{ 1}{\sqrt n}$
Now, $\lim\limits_{n \to \infty}\dfrac{a_n}{b_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{5^n}{\sqrt n4^n}}{\dfrac{ 1}{\sqrt n}}$
Thus, we have $ =\lim\limits_{n \to \infty} \dfrac{\sqrt n 5^n}{\sqrt n4^n}$
or, $=\infty$
Hence, the series is divergent due to the limit comparison test.
