Chapter 11 - Infinite Sequences and Series - 11.6 Absolute Convergence and the Radio and Root Tests - 11.6 Exercises - Page 782: 1

(a) divergent (b) absolutely convergent (c) could converge or diverge

a) By the definition of the ratio test, $r\gt1 $ and thus the series must diverge. b) Since r is less than 1, the series is absolutely convergent by the ratio test. c) The ratio test fails when $r=1$. So the series could converge or diverge