Answer
The series $\sum_{n=1}^{\infty} \frac{1}{4^n}$ converges.
Work Step by Step
To apply the root test, we have
$$
L=\lim _{n \rightarrow \infty} \sqrt[n]{a_{n}}=\lim _{n \rightarrow \infty} \sqrt[n]{1/4^n}=1/4\lt 1
$$
Hence the series $\sum_{n=1}^{\infty} \frac{1}{4^n}$ converges.
