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Convergence of a series

  • #1

Homework Statement


Find the radius of convergence and the interval of convergence for
[tex]
\sum_{n=0}^\infty \frac{x^n}{n3^n}

[/tex]



Homework Equations





The Attempt at a Solution


Ok, so I first applied the ratio test.
[tex]
\lim_{n\rightarrow\infty}

|
\frac{x^{n+1}}{(n+1)3^(n+1)} /
\frac{x^n}{n3^n}
|
[/tex]

After some cancellations I got

[tex]
L = |x/3|

[/tex]


Does this mean that the interval of convergence is from -3<x<3 ?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Yes.
 
  • #3
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
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99
You have to check the endpoints of your interval separately to see if the series converges there since the ratio test doesn't give any information when the limit is 1
 

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