Question

8) Solve only 6 of the questions A-J. Mark the questions you want graded. Determine if each of the infinite series below is converging or diverging. If you do not identify the method you use you receive a maximum of 1 point. A. (-1)"sin (Ln) B. E cos(Fn) c. Stan (n/(T-H)) D. Esin(n+1)/n 1 1 E. H/(nº+(F+L)n+ F*L) G. [T/(T-L)) F. ΤΣ S n=F+L (n-F)(n+L) ni H. (/(T-e) )-H 1. (n+L)/(n2+(L+H)n+L*H) J. [(H/F)n+(L/H)-1 I 1

H= 6

T=25

F= 2

L=2

S=45

Answer 1

ร nai L= 2 J { (-1. Sinan shi the sessies is alternating. Sinan ,داد لا Un clearly sunt is not a monotonii le <sinan> is oscilating sequence. and also lim Sinan does not enlist thus sein. Sinan is divergent. nas nza cos (rn) Let F = 2 WE 3 l cosan n=1 let Una Cosan n it San cleusly <cosand is oscilating requinie then I'm cos?n does not exist & then limento do is convergent thus Ĉ cosan is tivergent ny Gin nel nas

E E H n=1 n²+(FtldntFol Let H=6 F = २ L=2. 6 & W & naohitanta let Un = 6 n² tant 4 Vn 5 h2 Un ons h² tanta lim un lim nos Vn q n het lim Un nyo Vn = 6 to 6 to (tinite) limit Comparifion test thus by 2 6 ngh'tanta is convergent as 18 Convergent. n=b h

T S 35 n=ft (n-fjinta) let T=25 SE 45 T - 2, L=2 = swa ST h=FAL n²+nL-Fn-FL = Š ST htu-F) FL n=ftl let Un 11 ST n²+(1-F)n-F*L va t's lim un ar = lim ST (2) thus n=F+L(0-F) (nais by limit compurision test. m2 (i+(l-F) + (firme ST = nonzero finite is convergent

swa FJ" Let una T Tin Unl lim luni Il IL n> In lim luni = 25-2 S. nases so by dood test & J is convergent. I E (+2) let un n=in²+(1+H)N+LEH nth n²+ (6 + H)n + L+H Let un 11 ñ Un n²tln n²+ (1+H)n +LxH lim Uni no Val lim itin El It (L+H) + Lt thus by limit cum bursiun test on is divergent as 8 vn is divergent. gwa