I have used the ratio test for series.
Let $a_n = \frac{n^4}{4^n}$
Therefore $\lim_{n\to\infty}| \frac{a_{n+1}}{a_n} |= \lim_{n\to\infty} \frac{(n+1)^4}{4^{(n+1)}} * \frac{4^n}{n^4}$
= $\lim_{n\to\infty} \frac{(n+1)^4}{4n^4} = |\frac{1}{4} | $
Since the ratio is less than 1, the series converges.
Is this correct?