Series comparison test question

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Homework Help Overview

The discussion revolves around the convergence of the series defined by the summation from n=1 to infinity of (e^(1/n)) / n, which falls under the topic of series convergence tests in calculus.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster seeks guidance on which convergence test to apply, considering a comparison test with a chosen series. Some participants affirm the comparison and discuss the relationship between the terms of the series.

Discussion Status

Participants are actively engaging with the original poster's approach, confirming the comparison made and discussing the implications of the terms involved. There is an emphasis on providing a more rigorous justification for the assumptions made regarding the terms of the series.

Contextual Notes

There is a mention of the need for a stronger rationale for the inequality e^(1/n) > 1, indicating a potential gap in the original poster's reasoning that is being explored in the discussion.

cue928
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Homework Statement


Summation from n=1 to infinity: (e^(1/n)) / n


Homework Equations





The Attempt at a Solution



Can someone point out what criteria I should be considering when trying to determine which test to use? I was looking at a comparison test as a way to go on this one. I'd chosen an = (e^(1/n))/n and bn = 1/n. Since bn is a divergent p-series then an should also be divergent. Am I on the right track there?
 
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Yes. an>bn, right?
 
Last edited:
Yes, just testing out the first few terms, yes, an>bn, so the series an is divergent.
 
cue928 said:
Yes, just testing out the first few terms, yes, an>bn, so the series an is divergent.

You might want to try to give a better reason why e^(1/n)>1 than just testing the first few terms.
 

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