hw91 - 9.1 Pages 453-454 # 1-17odd, 21-29 odd 1. 1 2 3 4 5...

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9.1 Pages 453-454 # 1-17odd, 21-29 odd 1. 1234 5 5 , 2581 1 1 4 aa aa a ==== = 1 11 lim lim ; 3– 1 3 nn n n n →∞ →∞ == converges 11. 3. 12 3 61 83 8 2, 391 7 aa a = = = 45 66 22 102 34 27 9 39 13 = = 2 2 2 2 23 1 4 42 lim lim 4; 1– 1 n n n n →∞ →∞ + + + + converges 24 2.4630, 6.0665, 39 ee =≈ 68 34 23.7311, 110.4059, 17 27 10 5 564.7812 39 e a Consider 22 2 2 lim lim lim 2 1 xx x x e x →∞ →∞ →∞ = + + by using l’Hôpital’s Rule twice. The sequence diverges. 5. 3 72 66 3 , 82 76 4 a = 124 215 125 216 32 33 2 lim lim (1 ) 3 31 nnn n n →∞ →∞ ++ = + + 2 1 1 lim 1 1 n n n n →∞ ++ + 13. 2 –0.6283, 0.3948, 52 5 ππ –0.2481, 0.1559, 125 625 = 5 5 –0.0979 3125 a π (– ) , – 1 1, 55 5 n n n π  = <<   thus the sequence converges to 0. 7. 1 2 , 2 56 3 = = 5 5 7 a = 2 1 lim lim 2 1 n n n →∞ →∞ + + but since it alternates between positive and negative, the sequence diverges. 15. 3 2.99, 2.9801, 2.9703, a = 2.9606, 2.9510 (0.99) n converges to 0 since –1 < 0.99 < 1, thus 2 (0.99) n + converges to 2. 9. 123 –1, aaa = = = ()() cos 1 n n π =− , so 1c o s ()1 .
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hw91 - 9.1 Pages 453-454 # 1-17odd, 21-29 odd 1. 1 2 3 4 5...

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