Question

1. State whether the following statements are true or false. Give reasons for your answer (a) If limko WR=0 then our converges (b) = 5 means that the partial sums converge to 5 (c) E U is called conditionally convergent if it satisfies the conditions of the alternating series test (d) The limit comparison test applies only to series which are positive from some point on (e) (-2)* = 5 (f) If uk = (2k + 1)! then uk+1 = (2k + 2)! (g) In the p test if p > 1 the series diverges (h) If all the terms of a series are positive then the series must converge or else go to infinity

Answer 1

1. Con (FALSE) eye te series diverges but him to K & K senies divenges sy p-senies test of sum the ux conies is same (6) (TRUE) I KSI I as the limit of partial ( (FALSE) The definition of is [o ex is convergent sum by definition. conditionally convengent and coluk) is koo ic= 0 test applies to positive & divergent. FALSE) Limit comparison term series only. co Ezkling :( lim K to Lim Galk k so 3 k (2-1) is FALSG E wt 9 + is a , , p, Cenu 4. (6) = (2x + 1)! ukti - (2 K+1) + 1) = (2x + 3)! FALSE

G FALSE po series test P71 Y renies an diverges. Ch Trene kso Ireny positive series is associated with the sequence of pantial sum. E ek is given Senies. (Sk) say its sequence of pantial sum. & Sk = not wit – tuki Skti s lo tuyt een & uk cleanly sk s Skt . so (Sk) is a monotincally increating sequence of it is bounded above then conrengent otherwise divergent, but it never oscillates. Limet of sequence of pantial sum is sum of the renies. So series behaves like sequence of pantial sum.