Does the Series 1.05^n/n^5 Converge or Diverge?

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Homework Help Overview

The discussion revolves around the convergence or divergence of the series defined by the summation from 1 to infinity of 1.05^n/n^5, which falls under the subject area of series convergence tests in calculus.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about applying the ratio test and convergence tests in general. Some participants question the limit of the series' terms as n approaches infinity, while others suggest that it approaches infinity, leading to a conclusion about divergence.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the limit of the series' terms. While some guidance has been offered regarding the behavior of the limit, there is no explicit consensus on the final conclusion.

Contextual Notes

Participants are navigating the complexities of convergence tests and the implications of limits, indicating a need for clarity on these concepts.

lmannoia
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Homework Statement



Summation from 1 to infinity of 1.05^n/n^5

Homework Equations





The Attempt at a Solution


Lost. I'm not sure if the ratio test would apply here.. convergence tests are definitely not my strong point!
 
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Does the limit of \frac{1,05^n}{n^5} approach 0? What can you conclude from this?
 
No, it would approach infinity, right? Meaning that it diverges?
 
Yes, so you can conclude that the series diverges.
 

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