Radius of Convergence Problem with Solution Attempt

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Homework Help Overview

The discussion revolves around a problem related to the radius of convergence for a series, with participants exploring the implications of factorial terms in their attempts to find a solution.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are examining the form of the an+1 term and questioning the presence of the factorial in the numerator. There is also a discussion about the implications of the radius of convergence and the resulting interval.

Discussion Status

Some participants have provided guidance on checking specific terms in the series, while others are verifying their understanding of the radius of convergence and its implications. Multiple interpretations of the results are being explored.

Contextual Notes

There are references to figures that are not visible in the discussion, which may contain critical information for understanding the problem setup. Participants are also navigating the constraints of homework rules regarding solution completeness.

jegues
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Homework Statement



See figure attached for problem statement as well as my attempt.

Homework Equations





The Attempt at a Solution



See 2nd figure attached.

I don't know how to rid myself of that last n! I've got kicking around in the numerator.

Any ideas?
 

Attachments

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  • ROCQ1A1.jpg
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Check your an+1 term. The [(n+1)!] should be squared.
 
jav said:
Check your an+1 term. The [(n+1)!] should be squared.

Doh!

Thank you!
 
Just to make sure I finished the question off right, we should find that R = -1, correct?

Then the open interval of convergence is,

[tex]|x-7| < -1[/tex]

or [tex]1 < x-7 < -1[/tex] or [tex]8 < x < 6[/tex]
 

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