The alternating series test is a theorem which says the following: If a series a1 - a2 + a3 - 04 + 05 - ... satisfies (1) an > 0, (2) an 2 an+1 and (3) lim, too an = 0, then the series converges. Very powerful and very useful. For example, the series + 091 H satisfies (1), (2), and (3). a) Give an example of a divergent series that satisfies (1) + (3) but not (2). b) Give an example of a divergent series that satisfies (1) + (2) but not (3)