Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Another proof by induction

  1. Oct 16, 2004 #1

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Basically I will have won if I can show that

    [tex]n+1 \geq \left( 1+ \frac{1}{n} \right)^n[/tex]

    can I? Not that I haven't tried...

    This is also equivalent to showing that

    [tex]n^n \geq (n+1)^{n-1}[/tex]
     
    Last edited: Oct 16, 2004
  2. jcsd
  3. Oct 16, 2004 #2

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I found it. It wasn't so easy but it turns out that the sequence on the right has 3 for an upper bound. More precisely, it has e, the neperian number, has its supremum. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Another proof by induction
  1. Proof by Induction (Replies: 7)

  2. Proof by Induction (Replies: 2)

Loading...