Radius of convergence

  • Thread starter aydin
  • Start date
  • #1
aydin

Homework Statement



find the radius of convergence and interval of convergence of the series


Σ (3x-2)^2 / n 3^n
n=1


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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You need to clean up your notation a little bit, but the ROC for this series is easily found using any number of tests. Try the ratio test or the limsup test.
 
  • #3
HallsofIvy
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[tex]\sum_{n=1}^\infty \frac{(3x-2)^n}{n n!}[/tex]
is, I think, what you want.

Ratio test is probably best.
[tex]a_n= \frac{|3x-2|^n}{n n!}[/tex]
and
[tex]a_{n+1}= \frac{|3x-2|^{n+1}}{(n+1) (n+1)!}[/tex]

so the ratio is
[tex]\frac{|3x-2|^{n+1}}{(n+1)(n+1)!}\frac{n n!}{|3x-2|^n}= |3x-2|\frac{n}{(n+1)^2}[/tex]
What is the limit of that as n goes to infinity? If that is less than 1, the series will converge.
 

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