Answer
Converges
Work Step by Step
Apply the ratio test to the series
$\Sigma^{\infty}_{n=1} \frac{n}{4^n}$
$\lim\limits_{n \to \infty} |\frac{\frac{n+1}{4^{n+1}}}{\frac{n}{4^n}}|$, All values are positive
$\lim\limits_{n \to \infty} \frac{n+1}{4n} = \frac{1}{4} \lt 1$
Because the answer is less than one, the series converges
