Question

5. Determine if the following series converges absolutely, converges conditionally, or diverges? (-1)*+1m2 n-1 b.

Answer 1

Absolute A Convergence: series Ean converges of the absolute es absolutely values, if the series Eland converger. (-1)+1 no 2 E | Eight) nr ns2 n1 E n3-1 n? n3 n-a E ne2

hormoni series and lalell, this for alternating be it diverges. so now series test go bn where, (-1)+1 an - no & bn= 22 So bn=1 and, lim I = 0 bn lim n--> 00 na & this decreasing series [bnti converges. So bn] alternating series given conditional convergent series So series the

(10) E (1) ES nel with go absolute ratio test dim (-0) n+1 3nt) (-1) an Jan 01 lim 30+) 3n (n+1)! x lim on (n+1) "so, L<1 3 lim nti series converges abodutely thes As n-)