4. Each of the following series diverges. For each, choose the first listed reason, from the order given, that may be used to justify that the series diverges. If you choose reason (i), (ii), (iii), or (v), then give the additional information requested. Possible reasons: (i) The series is a divergent geometric series (give the common ratio r). (ii) The series is a divergent p-series (identify p). (iii) The series diverges by the divergence test (find the limit of an). (iv) The series diverges by the ratio or root test (p > 1). (v) The series diverges by the (limit or direct) comparison test, comparing with a divergent p-series (give the p-series you would compare with). (a) (b) n=2 8 n.5 - 1 3+n6 n=1 1 n²/3

4. Each of the following series diverges. For each, choose the first listed reason, from the order given, that may be used to justify that the series diverges. If you choose reason (i), (ii), (iii), or (v), then give the additional information requested. Possible reasons: (i) The series is a divergent geometric series (give the common ratio r). (ii) The series is a divergent p-series (identify p). (iii) The series diverges by the divergence test (find the limit of an). (iv) The series diverges by the ratio or root test (p > 1). (v) The series diverges by the (limit or direct) comparison test, comparing with a divergent p-series (give the p-series you would compare with). (a) (b) n=2 8 n.5 - 1 3+n6 n=1 1 n²/3

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 81E

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