## Calculus (3rd Edition)

The series $\sum_{n=1}^{\infty} \frac{1}{3^{n^2}}$ converges.
We compare the given series $\sum_{n=1}^{\infty} \frac{1}{3^{n^2}}$ with the geometric series $\sum_{n=1}^{\infty} \frac{1}{3^{n}}$ which is a convergent series ($r=\frac{1}{3}\lt 1$). Thus, by the comparison test, the given series $\sum_{n=1}^{\infty} \frac{1}{3^{n^2}}$ also converges.