Question

Which of the following series are conditionally convergent? o - no (1) E(-1, (u) į(-1)" VA n= 4 n2+1 (1), (11), and (iii) (i) and (III) only (i) and (ii) only (11) only (1) only (i) and (ill) only (iii) only

Answer 1

. Given Se Series na 03H no 2 Take absolute series n3H11 0 120 ampare 20 ne no Have about serves a yo Še many of his Compose it with her and then une noch assume that then that alimentatia hind option H1 (o, finite) 3 by limit compartsion test , both series e en and va beshave be baice alive by po test ma is diversent Series * Šun - Duration is divergent Series by Lebnitz test this is convergent Series je Series I own any is egti Conditionally cat. no no verrae 2

Š (- un 'n of n2 maitaj Sey take crashake series Compose with the us are then we get then we get Compare with am let) costume fm - assume n2 - lim l isñ = 1 AJ M CUT n 22 di verra n2 naz 2 by limit Comportsion test . both series behave alike is by potest v is divergent + EUR = region is divergent Series by Lesnity test co la convergent Series Serien Ž -19. is Conditionally Convergent. erg n2 2 Series 1. Condition nh

take absolute Service take absolute Series & mehr - n²H ADŲ n24 Berit Compose this series with a un es then una in . 2 (1 assume noa 4 11cm nau 1. behave alike 4 Vur a by limit compariston test both series on and on .by potest v is convergent * 3 un is convergent ** Series E co is absolutely Convergent - [only ů and chill Conditionally convergent onven neu