Answer
Yes, the series $\Sigma_{n=1}^{\infty}a_n^{-1}$ converges.
Work Step by Step
Let $b_n=a_n^{-1}$; then applying the ratio test, we have
$$
\rho=\lim _{n \rightarrow \infty}\left|\frac{b_{n+1}}{b_{n}}\right|=\lim _{n \rightarrow \infty} \left|\frac{a_{n+1}^{-1}}{a_{n}^{-1}}\right|\\
=\lim _{n \rightarrow \infty} \left|\frac{a_{n } }{a_{n+1}}\right|=\frac{1}{4}\lt1
$$
Hence, the series $\Sigma_{n=1}^{\infty}a_n^{-1}$ converges.
