117 - MATH 153 Selected Solutions for §11.7 I’m doing...

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Unformatted text preview: MATH 153 Selected Solutions for §11.7 I’m doing this section differently; instead of giving a select few answers, I’m going to give all answers along with the test used to derive that answer. Feel free to ask for clarification on any problem. CT = Comparison Test, LCT = Limit Comparison Test, IT = Integral Test, DT = Divergence Test, AST = Alternating Series Test, RaT = Ratio Test, RoT = Root Test. Converges; CT/LCT with Converges; RoT Diverges; DT or AST Converges; AST Converges; RaT/RoT 1 3n Exercise Exercise Exercise Exercise Exercise 1: 2: 3: 4: 5: Exercise Exercise Exercise Exercise Exercise 1 6: Diverges; LCT with n 7: Diverges; IT 8: Diverges; RaT 9: Converges; IT or RaT/RoT 10: Converges; IT or RaT/RoT Exercise Exercise Exercise Exercise Exercise 11: 13: 14: 15: 16: Converges; AST Converges; RaT Converges; CT with Converges; RaT Diverges; LCT with Exercise Exercise Exercise Exercise Exercise 17: 18: 19: 20: 21: Diverges; DT or AST Converges; AST Converges; AST Converges; RaT/RoT Converges; RoT Exercise Exercise Exercise Exercise 22: 24: 25: 26: Converges; CT/LCT with Diverges; DT Converges; RaT Converges; RaT/RoT 1 2n (first take absolute value) 1 n 1 1 n2 2 Exercise 27: Converges; CT with Exercise Exercise Exercise Exercise Exercise 28: 30: 31: 32: 33: k ln k k3 = lnk k2 followed by IT on e Converges; CT with n2 or LCT with Converges; AST n Diverges; CT with 254n · Diverges; DT or RoT 1 Diverges; LCT with √n Exercise 34: Diverges; CT/LCT with 21 n Exercise 35: Converges; RoT (lim = 1 ) e Exercise 37: Converges; RoT 1 n2 ln k k2 ...
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This note was uploaded on 07/26/2011 for the course MATH 153 taught by Professor Rempe during the Spring '08 term at Ohio State.

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117 - MATH 153 Selected Solutions for §11.7 I’m doing...

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