Question

2.0, so in the contention, butun she 3. (10), 10, 10) For each series, determine whether it converges absolutely, converges conditionally, or diverges. Justify your answer, including naming the convergence test you use. can reduce res conditionally 2

Answer 1

n2 Y Inch a 102 a) = = an (let) It is an alternating series such that an> antiso So using Alternating seris testię lima lan1=0 Stor hvor lenge me ane te Chine) 20 convergent = for absolutly comergent Elanl should be covergent so Elanl= & a fusing P-serine test Here n=3 n²(ln(h. I p=2> loilo it is conveges. an is absolutely covergent. nyt hs being o

Bl e hy as an n=2 Wire comprision method - loe lim. an-some constart. ۲ نمبر hool YA nso let bn = 1 1 1 1 1 1 1 1 so there are the one that *°) - Hatari = too l { constant, the finit so Ebn = 13 using P- series it is pinergent . Since P= // <1 so (Divergent). 1-0 n 7=2

2 § (k!, sean ko (2k) Voing Ratio test ie lim Taks per comergent 2K TO tim K? (1+kuje (1 to² 1 ks (2 K² (2 + 3) (2+1) +2 n (1+ k² (2 + 2/2) (2 + 1 i Asos (2+2 / 3 (2+1 = (2+07246) + =) <1 hence it is covergent El and is also connesgant so an is absolutely convergenta