At the end of Playlist 13, you learned about the Ratio Test. The main idea that underlies the Ratio Test is the following. One way to to characterize a geometric series is that the ratio between successive terms is constant. That is, be = ro for all n e N (i.e., _ be is a geometric series) if and only if bo = 1 and b, buti = r for all n E N. We also know that a geometric series _ r converges if and only if |r| 1, then _ an diverges. Hint. Start by using the definition of that limit to show that there is an r > 1 such that, for sufficiently large n, van > r. (c) Prove that if lim Van = L 1 or = oo, then _ on diverges. . If lim