Ratio Test for Radius of Convergence | Solving sum(5^n)((x-3)^n)/n"

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Homework Help Overview

The problem involves determining the radius of convergence for the series sum(5^n)((x-3)^n)/n, starting from n=1. The context is within the study of power series and convergence tests.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the ratio test and question the original poster's breakdown of the series. There is a focus on ensuring all components of the series are included in the analysis.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's approach and emphasizing the importance of including the 5^n factor in the calculations. There is no explicit consensus yet, as different interpretations of the problem are being explored.

Contextual Notes

Participants are navigating the requirements of the ratio test and ensuring that all elements of the series are accurately represented in the calculations. There may be assumptions about the familiarity with convergence tests that are being questioned.

thomas12323
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Homework Statement



The problem is looking for the radius of convergence
sum(5^n)((x-3)^n)/n
n=1

Homework Equations





The Attempt at a Solution

 
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What work have you done in using the ratio test?
 
I broke it down to (x-3)n/(n+1)
 
That's not right. What happened to the 5^n factor?
You should have this as part of your work.
[tex]\lim_{n \to \infty} \left(\frac{5^{n + 1}(x - 3)^{n + 1}}{n + 1}~\frac{n + 1}{5^n (x - 3)^n}\right )[/tex]
 

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