In your own words, explain how and why the Direct Comparison Test work in the way they do by answering the questions below. (b) Suppose En, an and En, bn are series with positive terms, and suppose _, an is known to be divergent. Suppose that an > b, for all n. Question: can we conclude anything about the series En on based on this information? To answer the question, give: (i) an explicit example of a pair of series _, an and E., br that satisfies the conditions given, where En an diverges and En by diverges, and (ii) an explicit example of a pair of series En a, and En, b,, that satisfies the conditions given, where En a, diverges and _,, bn converges. Explain, in your own words, how your two examples show that it is not possible to conclude anything about the series , b, based on the information that is given. 4