## Calculus (3rd Edition)

The series $\sum_{n=5}^{\infty} (4/5)^{-n}$ diverges.
We have $$\lim_{n\to \infty} (4/5)^{-n}=\lim_{n\to \infty} (5/4)^{n}=\infty.$$ Where we used the fact that $5/4\gt 1$. Hence, the series $\sum_{n=5}^{\infty} (4/5)^{-n}$ diverges.