Answer
(a) Divergent
(b) Absolutely Convergent
(c) Could converge or diverge
Work Step by Step
(a) Since $\lim\limits_{n \to \infty}\left|\frac{a_{n+1}}{a_n}\right|= 8 > 1$, we can conclude that the series $\sum{a_n}$ is divergent by the Ratio Test.
(b) Since $\lim\limits_{n \to \infty}\left|\frac{a_{n+1}}{a_n}\right|= 0.8 < 1$, the series $\sum{a_n}$ is absolutely convergent, and thus convergent, by the Ratio Test.
(c) Since $\lim\limits_{n \to \infty}\left|\frac{a_{n+1}}{a_n}\right|= 1 $, the Ratio Test is inconclusive. Therefore, the series $\sum{a_n}$ might converge or diverge.
