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Q. 16

Found in: Page 624


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.

k=1 1k

The divergence test failed as limk1k=0.

See the step by step solution

Step by Step Solution

Step 1. Given information.

Consider the given series,

k=1 1k

Step 2. Analyze the series.

The divergence test states that if the sequence ak does not converge to zero, then the series akk=1 diverges.

The value of the sequence ak=1k is given below,


Thus, the divergence test failed as limk1k=0.

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