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hw91 - 9.1 Pages 453-454 1-17odd 21-29 odd 1 1 2 3 4 5 a1 =...

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9.1 Pages 453-454 # 1-17odd, 21-29 odd 1. 1 2 3 4 5 1 2 3 4 5 , , , , 2 5 8 11 14 a a a a a = = = = = 1 1 1 lim lim ; 3 –1 3 3 – n n n n n →∞ →∞ = = converges 11. 3. 1 2 3 6 18 38 2, 2, , 3 9 17 a a a = = = = = 4 5 66 22 102 34 , 27 9 39 13 a a = = = = 2 2 2 2 2 3 1 4 4 2 lim lim 4; 1 3 –1 n n n n n n n n →∞ →∞ + + = = + + converges 2 4 1 2 2.4630, 6.0665, 3 9 e e a a = = 6 8 3 4 23.7311, 110.4059, 17 27 e e a a = = 10 5 564.7812 39 e a = Consider 2 2 2 2 2 4 lim lim lim 2 3 2 3 –1 x x x x x x e e e x x x →∞ →∞ →∞ = = = ∞ + + by using l’Hôpital’s Rule twice. The sequence diverges. 5. 1 2 3 7 26 63 , , , 8 27 64 a a a = = = 4 5 124 215 , 125 216 a a = = 3 2 3 2 3 3 2 3 3 3 3 lim lim ( 1) 3 3 1 n n n n n n n n n n n n →∞ →∞ + + + + = + + + + 2 2 3 3 3 3 3 1 1 lim 1 1 n n n n n n →∞ + + = = + + + 13. 2 1 2 –0.6283, 0.3948, 5 25 a a π π = = 3 4 3 4 –0.2481, 0.1559, 125 625 a a π π = = 5 5 –0.0979 3125 a π = (– ) , –1 1, 5 5 5 n n n π π π = < < thus the sequence converges to 0. 7. 1 2 3 4 1 2 1 3 4 2 , , , , 3 4 2 5 6 3 a a a a = = = = = = 5 5 7 a = 2 1 lim lim 1, 2 1 n n n n n →∞ →∞ = = + + but since it
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