(d) n=2 COS() For each of the following series decide if it is Absolutely Convergent, Conditionally Convergent, or Divergent. You must justify all answers. ∞ n (e) (-1) 3n+2n+7 (f) n=1 iM8 n=1 5n8-4n2 11+3sin(n) 2n-1 h=2 COS() 11+3sin(n) 11±3 F ~ 2n-1 2n-1 2n Diverges as a n=1 P-series. DCT. 11+3sin(n) NTS 2n-1 2n TED Tim n1-390 = Cos() Cos()=1+0. So this series Diverges by TED Proof 11 +35in(n) Since 2 2n-1 nce & Diverges Series 2n x11+3sin(n) 2n-1 h=1 8 20 as a p-series by DCT also diverges ทะเ (-1)" 344 +2n+7 558-452 Consider Elanl Root Test. lim n-78 /n Tim n-700 3n4+2n+7 518-452 17m 3n4+2n+7 1/48 5-4n2 408 1-700 Tim 9720 = 13/140 2/123047/483 5-4/4670 -12-1. <1 = A.C. く So by Root Test This series A. C