Question

5. Determine the convergence/divergence of the following series. If convergent, then give the exact value where possible. (40 points) 2- a) 2 - +3 102"+3 The Adventure Continues Again b) 2-anglen

Answer 1

22 ton let un 2 2-n+3 n 20 (14 3 2 lim un no una lim (1 (1 = lim no 2 3n -1 =10 Itin I to Then by divergent test não diverges] . X 03-4n りこ 23 51 sn 5 yo 57 nal n=1 nal 24h.si (24) n be a geometric series whose asteem, ac and common ratio,r= Hence, ĕ 23-4n sito convergess) nel and their sum i -) e un let una 2 2 4 wa - 2 m 2 ( 14 ) = - - 2 to asna x let vna 2 allows um = city) Here {un is convergent Then by limit comparison test Eun is also convergent Hence, e 2 [ { tp Converges if p>1] n=5 (n² un converges) Again, n=5 n(n-u) = 28 in- (0-4) 1 no5 n(n-w 9 na - - 1 5 -1 +1 2 1 6 +1 3 +1 4 -1 8 + 4 5 -1 g + -- - t I n-9 - 4 n-5 + 1 + n-8 sy 1 n - 1 n-3 7 + 1 n-6 - - 1 n-2 + 1 1-5 -1 + 7 n-1 nun) ( 1+1 +1 AL ī 2 3 4 as no =(12.76 +43) = GJ = 25 Hence is on 12 2u