Answer
The series $\sum_{n=1}^{\infty} (3/4n)^n$ converges.
Work Step by Step
To apply the root test, we have
$$
L=\lim _{n \rightarrow \infty} \sqrt[n]{a_{n}}=\lim _{n \rightarrow \infty} \sqrt[n]{(3/4n)^n}=\lim _{n \rightarrow \infty} \frac{3}{4n}=0\lt 1
$$
Hence the series $\sum_{n=1}^{\infty} (3/4n)^n$ converges.
