Answer
The series $\Sigma_{n=0}^{\infty} \frac{1}{10^n}$ converges.
Work Step by Step
To apply the root test, we have
$$
L=\lim _{n \rightarrow \infty} \sqrt[n]{a_{n}}=\lim _{n \rightarrow \infty} \sqrt[n]{1/10^n}=1/10\lt 1
$$
Hence the series $\Sigma_{n=0}^{\infty} \frac{1}{10^n}$ converges.
