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(a) Give an example of a series a, where_lim_|a|¹/" an where lim |an|1/n = 1 and Σan converges. 818 n=1 (b) Give an example of a series Σ an where lim |an|1/n = 1 and Σ a diverges. n=1 84u n=1 Note: These two examples show why in Root Test if the limit is equal to 1 we get NO INFORMATION

(a) Give an example of a series a, where_lim_|a|¹/" an where lim |an|1/n = 1 and Σan converges. 818 n=1 (b) Give an example of a series Σ an where lim |an|1/n = 1 and Σ a diverges. n=1 84u n=1 Note: These two examples show why in Root Test if the limit is equal to 1 we get NO INFORMATION

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 26RE
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(a) Give an example of a series a, where_lim_|a|¹/" an where lim |an|1/n = 1 and Σan converges. 818 n=1 (b) Give an example of a series Σ an where lim |an|1/n = 1 and Σ a diverges. n=1 84u n=1 Note: These two examples show why in Root Test if the limit is equal to 1 we get NO INFORMATION
Transcribed Image Text:(a) Give an example of a series a, where_lim_|a|¹/" an where lim |an|1/n = 1 and Σan converges. 818 n=1 (b) Give an example of a series Σ an where lim |an|1/n = 1 and Σ a diverges. n=1 84u n=1 Note: These two examples show why in Root Test if the limit is equal to 1 we get NO INFORMATION
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