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: Induction proof of an inequality

  1. May 8, 2010 #1
    1. The problem statement, all variables and given/known data

    for all integers n>=1, n! <= n^n

    2. Relevant equations

    3. The attempt at a solution

    Base case: (1)! <= (1)^(1) 1=1 check
    Inductive hypothesis: suppose k!<=k^k
    P(k+1): (k+1)! <= (k+1)^(k+1)

    From here on out I get very confused. Any help would be appreciated!
  2. jcsd
  3. May 8, 2010 #2


    User Avatar
    Homework Helper

    Write [itex](k+1)! \le (k+1)^{k+1}[/itex] in terms of k and k^k.
  4. May 8, 2010 #3
    so it would be k!(k+1) <= (k+1)^k + (k+1) ?
  5. May 8, 2010 #4


    User Avatar
    Homework Helper

    The right hand side is incorrect, but you're on the right track.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook