bn t N 0 008 N 12s N 1 0 008 08 N 1 5 N 1 4 v bn 1 c 3 0 008 L D3 0 008 minimum number of terms is 15 n 2n 2 2n n 1 2n 2 6 R 50 LLI so by Ratio test Series Converges Absolutely 3 series converges absolutely L so be Root test 3 2n TS 2 10 Lim n x 1 Lim n 2n 2 2n 1 2n S S 10 102 1 2n 2 2n 1 6 R Lim e O 4 Lc I so by Ratio test Converges Lim n x H n n 1 j a n 1 n n Lin n k 1 6 R n 1j nu at y 0 L 1 so by ratio test series converges 3 k y K Lim k 3 k Lim k 0S 3 T K 3 k D kt GR E 0 L 1 by So series ratio test converges absolutely neee L is So and finite Series n diverges 2n 3 O and diverges By AST Lin n 3 6 R 0 b AST it it Converses diverses so it by LCT but converges conditionally DNE nth term divergence series b diverges En 1x 1 in ca Lim n 0 Li i n 0 LCI so series by rootfest converge absolutely ente 1 21 Lim 2 n3 n h n In n S S 7 6 R n x n 1 n h Lim n n x L I so by ratio test series diverses SS