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: Series Comparison Test

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Find if the sum from n = 1 to infinity of (n^n)/n! diverges or not.

    2. Relevant equations

    p = an+1/an

    3. The attempt at a solution

    Using the comparison test I get to the point where p_n = (n+1)^(n+1) / [(n+1) n^n]

    Shouldnt p just be 0, dont (n+1)^(n+1) and n^n cancel for large n? The book says the answer is p = e, how do you get there?

    Thanks for the help!
  2. jcsd
  3. Oct 21, 2009 #2
    Why not try the ratio test?
  4. Oct 21, 2009 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    nn+1/nn doesn't cancel for large n, so when you replace nn+1 with (n+1)n+1 why would you expect it to?
  5. Oct 21, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    No, they don't cancel for large n. You are jumping to conclusions. If I look at your expression I would write it as (n+1)^n/n^n. Do you see how? Now what?
  6. Oct 21, 2009 #5


    User Avatar
    Homework Helper

    not zero, cancel the n+1 term
    [tex] \frac{(n+1)^{n+1}}{(n+1) n^n} = \frac{(n+1)^n}{n^n} = (\frac{n+1}{n})^n [/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook