1. Mar 28, 2010 #1

   nietzsche

   

   1. The problem statement, all variables and given/known data
   
   [tex]\text{Show that }\sum_{n=1}^{\infty} \left( \frac{e}{n} \right) ^n \text{converges.}[/tex]
   
   3. The attempt at a solution
   
   I think we should use the root test.
   
   [tex]\lim_{n \to \infty} \sqrt[n]{\left( \frac{e}{n} \right) ^n} = \lim_{n \to \infty} \frac{e}{n} = 0 < 1[/tex]
   
   So the series is convergent.
   
   
   Does it look alright?
   
   Thanks in advance.

    

   nietzsche, Mar 28, 2010
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3. Mar 28, 2010 #2

   Mark44

   

   Insights Author

   Staff: Mentor

   Looks fine.

    

   Mark44, Mar 28, 2010

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