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Homework Help: Convergence of series

  1. Mar 28, 2010 #1
    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.
  2. jcsd
  3. Mar 28, 2010 #2


    Staff: Mentor

    Looks fine.
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