Question

6. Classify each series as absolutely convergent, conditionally convergent, or divergent. a. (-1)* k Ink (5 pts) b. • (-1) 4+1 ! (2k - 1)! (5 pts)

Answer 1

(a) tuk w k=2 kenk 00 consider da ; ; put lna=t a lnx 2 dal=de ne dt t ent en2 ln2 . con ver Series is not tonditionally absolutely vergent. By Leibnitz test - 20 lim k you klink & is ар, decreasing Sequence conditionally convergent

classmate Date Page kat (6) ПМ (-1) 17 k! (26) ka clearly ak k! (2k-1)! is ultimately decreasing sequence DULU & lim K700 ak :. By leibnitz test Given Series is convergent

WOL class Date Page Colok 싸 (2 kt) 大功 k! ; Again aka 12k-)! kt (2k +) (2k-2)..... (k+Jk! = 2 (2k +)(2k-1) ... (h+

By comparison test with Mo kky ky Series is absolutely convergent