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Let a, = e8/n (a) Does the sequence {a,} converge or diverge? If it converges, find its limit. If it diverges, enter DIVERGES. (b) Determine whether the series a, converges. n=1 The series is convergent because it's a convergent geometric series. O The series diverges because it's a divergent geometric series. The series converges because it's a multiple of a convergent p-series. The series diverges because it's a multiple of a divergent p-series. The series converges by Divergence Test since lim an=0. O The series diverges by Divergence Test since lim a, + 0. n- 00 O O O O O

Let a, = e8/n (a) Does the sequence {a,} converge or diverge? If it converges, find its limit. If it diverges, enter DIVERGES. (b) Determine whether the series a, converges. n=1 The series is convergent because it's a convergent geometric series. O The series diverges because it's a divergent geometric series. The series converges because it's a multiple of a convergent p-series. The series diverges because it's a multiple of a divergent p-series. The series converges by Divergence Test since lim an=0. O The series diverges by Divergence Test since lim a, + 0. n- 00 O O O O O

Algebra & Trigonometry with Analytic Geometry
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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Let an : e8/n. = e (a) Does the sequence {a,} converge or diverge? If it converges, find its limit. If it diverges, enter DIVERGES. (b) Determine whether the series `a converges. n=1 The series is convergent because it's a convergent geometric series. The series diverges because it's a divergent geometric series. The series converges because it's a multiple of a convergent p-series. The series diverges because it's a multiple of a divergent p-series. The series converges by Divergence Test since lim an=0. n- 00 The series diverges by Divergence Test since lim an + 0. n- co
Transcribed Image Text:Let an : e8/n. = e (a) Does the sequence {a,} converge or diverge? If it converges, find its limit. If it diverges, enter DIVERGES. (b) Determine whether the series `a converges. n=1 The series is convergent because it's a convergent geometric series. The series diverges because it's a divergent geometric series. The series converges because it's a multiple of a convergent p-series. The series diverges because it's a multiple of a divergent p-series. The series converges by Divergence Test since lim an=0. n- 00 The series diverges by Divergence Test since lim an + 0. n- co
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