Question

87. If 0 <b, <an for n 2 1, which of the following must be true? (A) r Ιται α, = 0, then Σο, εοπνετραει. (0) Σε, εσεναρα, ελπι ίτι ό, το « «Σο, αντρας, θέση είτε , (0) Σο, αίνετρα, then Σ», ίνειρες. (E) 1ΗΣ, εοπνετges, then Σε, εοπνεrges. liverges, then diverges. converges, then n converges.

Answer 1

no 74.00 *. If Ean converges, then lim an=o. 1. But lim anao is not sufficient to ensure convergence of Ean. * Comparison Testi et can be a positive term series. - If an sa For na Nole IN), and - if sin converges, then can converges. - If an zdn>o for na Nolfind and it. [dn diverges, then Ean diverges. 87) If os bocan , for n>,l. Clearly, san and Ebri are positive term series, (Al. If limaro , then it does not say anything about the convergence of Ean. So, the comparison test can not be used. to arrive at the conclusion of convergence OF Ebni. (FALSE). (B? If San Converges, then by comparison test {bn converges. If Ebn converges, then lim bn =o. . (TRUE). (6) If Ebn diverges, then by comparison - م nta test, Ean diverges, which can not Say anything about lim an. (FALSE), mtu

(0) If Ean diverges, then nothing can be said about the convergence of Ebn. (FALSE) ②. If Ebn converges, then nothing can be . said about the convergence of san - (FALSE). Hence, the correct option is (B)..