1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Mark44

    Staff: Mentor

    Looks fine.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook