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: Is this proof for convergence of 3^n/n! rigorous enough?

  1. Sep 16, 2012 #1

    I am trying to self study analysis and was practicing some problems. I wasn't sure if this solution to one of the problems I came across was rigorous enough.

    Basically, by writing down the first few terms of 3^n and n!, I figured I can say 3^n < 3*(n-1)! for all n>=13...without actually calculating the numerical values.

    so (3^n/n!)<3/n for n>=13. Therefore, for any ε we can can find N>13 and N>3/ε. And therefore the term 3^n/n! converges to 0. Is this a right solution? Is it rigorous enough? Could you advise me of a better way to prove this?

    Last edited: Sep 16, 2012
  2. jcsd
  3. Sep 16, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You can prove it by induction. First, you can establish it is true for n = 8. So assuming it is true for n = k >= 8, prove it is also true for n = k+1. (This is EASY.) Thus, it is true for all n ≥ 8.

  4. Sep 16, 2012 #3
    I assume, you mean, to prove that 3^n<3(n-1)! for all n>=8. I guess that makes sense..Thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook